\documentclass[10pt,letterpaper]{article} \usepackage[top=0.85in,left=2.79in,footskip=0.79in,marginparwidth=2in]{geometry} \usepackage{amsmath, amsthm, amscd, amsfonts, amssymb, graphicx, tikz, color} \usepackage[bookmarksnumbered, colorlinks, plainpages]{hyperref} % use Unicode characters - try changing the option if you run into troubles with special characters (e.g. umlauts) \usepackage[utf8]{inputenc} % clean citations \usepackage{cite} % hyperref makes references clicky. use \url{www.example.com} or \href{www.example.com}{description} to add a clicky url \usepackage{nameref,hyperref} % line numbers \usepackage[right]{lineno} % improves typesetting in LaTeX \usepackage{microtype} \DisableLigatures[f]{encoding = *, family = * } % text layout - change as needed \raggedright \setlength{\parindent}{0.5cm} \textwidth 5.25in \textheight 8.79in % Remove % for double line spacing %\usepackage{setspace} %\doublespacing % use adjustwidth environment to exceed text width (see examples in text) \usepackage{changepage} % adjust caption style \usepackage[aboveskip=1pt,labelfont=bf,labelsep=period,singlelinecheck=off]{caption} % remove brackets from references \makeatletter \renewcommand{\@biblabel}[1]{\quad#1.} \makeatother % headrule, footrule and page numbers \usepackage{lastpage,fancyhdr,graphicx} \usepackage{epstopdf} \pagestyle{myheadings} \pagestyle{fancy} \fancyhf{} \rfoot{\thepage/\pageref{LastPage}} \renewcommand{\footrule}{\hrule height 2pt \vspace{2mm}} \fancyheadoffset[L]{2.25in} \fancyfootoffset[L]{2.25in} % use \textcolor{color}{text} for colored text (e.g. highlight to-do areas) \usepackage{color} % define custom colors (this one is for figure captions) \definecolor{Gray}{gray}{.25} % this is required to include graphics \usepackage{graphicx} % use if you want to put caption to the side of the figure - see example in text \usepackage{sidecap} \usepackage{leftidx} % use for have text wrap around figures \usepackage{wrapfig} \usepackage[pscoord]{eso-pic} \usepackage[fulladjust]{marginnote} \reversemarginpar \newtheorem{theorem}{Theorem}[section] \newtheorem{lemma}[theorem]{Lemma} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{corollary}[theorem]{Corollary} \theoremstyle{definition} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{xca}[theorem]{Exercise} \theoremstyle{remark} \newtheorem{remark}[theorem]{Remark} \theoremstyle{observation} \newtheorem{observation}[theorem]{Observation} \theoremstyle{question} \newtheorem{question}[theorem]{Question} \theoremstyle{problem} \newtheorem{problem}[theorem]{Problem} \numberwithin{equation}{section} % document begins here \begin{document} \vspace*{0.35in} \linenumbers % title goes here: \begin{flushleft} {\Large \textbf\newline{ SuperHyperMatching By (R-)Definitions And Polynomials To Monitor Cancer's Recognition In Neutrosophic SuperHyperGraphs } } \newline % authors go here: Henry Garrett \\ \bigskip DrHenryGarrett@gmail.com \\ \bigskip Twitter's ID: @DrHenryGarrett $|$ \copyright DrHenryGarrett.wordpress.com \end{flushleft} \section*{ABSTRACT} In this research, new setting is introduced for new SuperHyperNotions, namely, a SuperHyperMatching and Neutrosophic SuperHyperMatching . Two different types of SuperHyperDefinitions are debut for them but the research goes further and the SuperHyperNotion, SuperHyperUniform, and SuperHyperClass based on that are well-defined and well-reviewed. The literature review is implemented in the whole of this research. For shining the elegancy and the significancy of this research, the comparison between this SuperHyperNotion with other SuperHyperNotions and fundamental SuperHyperNumbers are featured. The definitions are followed by the examples and the instances thus the clarifications are driven with different tools. The applications are figured out to make sense about the theoretical aspect of this ongoing research. The ``Cancer's Recognition'' are the under research to figure out the challenges make sense about ongoing and upcoming research. The special case is up. The cells are viewed in the deemed ways. There are different types of them. Some of them are individuals and some of them are well-modeled by the group of cells. These types are all officially called ``SuperHyperVertex'' but the relations amid them all officially called ``SuperHyperEdge''. The frameworks ``SuperHyperGraph'' and ``neutrosophic SuperHyperGraph'' are chosen and elected to research about ``Cancer's Recognition''. Thus these complex and dense SuperHyperModels open up some avenues to research on theoretical segments and ``Cancer's Recognition''. Some avenues are posed to pursue this research. It's also officially collected in the form of some questions and some problems. Assume a SuperHyperGraph. Then a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; a neutrosophic R-SuperHyperMatching $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; a neutrosophic R-SuperHyperMatching SuperHyperPolynomial $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. Assume a SuperHyperGraph. Then $\delta-$SuperHyperMatching is a maximal of SuperHyperVertices with a maximum cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ there are $|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta;$ and $ |S\cap N(s)| |S\cap (V\setminus N(s))|_{neutrosophic}+\delta;$ and $ |S\cap N(s)|_{neutrosophic} , x\in X\}$$ where the functions $T, I, F: X\rightarrow]^-0,1\leftidx{^+}{[}$ define respectively the a \textbf{truth-membership function}, an \textbf{indeterminacy-membership function}, and a \textbf{falsity-membership function} of the element $x\in X$ to the set $A$ with the condition $$\leftidx{^-}{0} \leq T_A(x)+I_A(x)+F_A(x)\leq 3^{+}.$$ The functions $T_A(x),I_A(x)$ and $F_A(x)$ are real standard or nonstandard subsets of $]^-0,1\leftidx{^+}{[}.$ \end{definition} \begin{definition}[Single Valued Neutrosophic Set](\textbf{Ref.}\cite{5},Definition 6,p.2).\\ Let $X$ be a space of points (objects) with generic elements in $X$ denoted by $x.$ A \textbf{single valued neutrosophic set} $A$ (SVNS $A$) is characterized by truth-membership function $T_A(x),$ an indeterminacy-membership function $I_A(x),$ and a falsity-membership function $F_A(x).$ For each point $x$ in $X,$ $T_A(x),I_A(x),F_A(x)\in [0,1].$ A SVNS $A$ can be written as $$A = \{, x\in X\}.$$ \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued neutrosophic set $A = \{, x\in X\}$:$$T_A(X)=\min[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=\min[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=\min[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued neutrosophic set $A = \{, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)> 0\}.$$ \end{definition} \begin{definition}[Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{4},Definition 3,p.291).\\ Assume $V'$ is a given set. A \textbf{neutrosophic SuperHyperGraph} (NSHG) $S$ is an ordered pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued neutrosophic subsets of $V';$ \item[$(ii)$] $V=\{(V_i,T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)):~T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n'}\}$ a finite set of finite single valued neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i'},T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})):~T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})\geq0\},~(i'=1,2,\ldots,n');$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i'}\neq\emptyset,~(i'=1,2,\ldots,n');$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i'}supp(E_{i'})=V,~(i'=1,2,\ldots,n');$ \item[$(ix)$] and the following conditions hold: $$T'_V(E_{i'})\leq\min[T_{V'}(V_i),T_{V'}(V_j)]_{V_i,V_j\in E_{i'}},$$ $$ I'_V(E_{i'})\leq\min[I_{V'}(V_i),I_{V'}(V_j)]_{V_i,V_j\in E_{i'}},$$ $$ \text{and}~F'_V(E_{i'})\leq\min[F_{V'}(V_i),F_{V'}(V_j)]_{V_i,V_j\in E_{i'}}$$ where $i'=1,2,\ldots,n'.$ \end{itemize} Here the neutrosophic SuperHyperEdges (NSHE) $E_{j'}$ and the neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued neutrosophic sets. $T_{V'}(V_i),I_{V'}(V_i),$ and $F_{V'}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the neutrosophic SuperHyperVertex (NSHV) $V_i$ to the neutrosophic SuperHyperVertex (NSHV) $V.$ $T'_{V}(E_{i'}),T'_{V}(E_{i'}),$ and $T'_{V}(E_{i'})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the neutrosophic SuperHyperEdge (NSHE) $E_{i'}$ to the neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii'$th element of the \textbf{incidence matrix} of neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'}))$, the sets V and E are crisp sets. \end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{4},Section 4,pp.291-292).\\ Assume a neutrosophic SuperHyperGraph (NSHG) $S$ is an ordered pair $S=(V,E).$ The neutrosophic SuperHyperEdges (NSHE) $E_{i'}$ and the neutrosophic SuperHyperVertices (NSHV) $V_i$ of neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} \item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{HyperEdge}; \item[$(v)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} If we choose different types of binary operations, then we could get hugely diverse types of general forms of neutrosophic SuperHyperGraph (NSHG). \begin{definition}[t-norm](\textbf{Ref.}\cite{3}, Definition 5.1.1, pp.82-83).\\ A binary operation $\otimes: [0, 1] \times [0, 1] \rightarrow [0, 1]$ is a \textbf{$t$-norm} if it satisfies the following for $x,y,z,w \in [0, 1]$: \begin{itemize} \item[$(i)$] $1 \otimes x =x;$ \item[$(ii)$] $x \otimes y = y \otimes x;$ \item[$(iii)$] $x \otimes (y \otimes z) = (x \otimes y) \otimes z;$ \item[$(iv)$] If $ w \leq x$ and $y \leq z$ then $w \otimes y \leq x \otimes z.$ \end{itemize} \end{definition} \begin{definition} The \textbf{degree of truth-membership}, \textbf{indeterminacy-membership} and \textbf{falsity-membership of the subset} $X\subset A$ of the single valued neutrosophic set $A = \{, x\in X\}$ (with respect to t-norm $T_{norm}$):$$T_A(X)=T_{norm}[T_A(v_i),T_A(v_j)]_{v_i,v_j\in X},$$ $$I_A(X)=T_{norm}[I_A(v_i),I_A(v_j)]_{v_i,v_j\in X},$$ $$ \text{and}~F_A(X)=T_{norm}[F_A(v_i),F_A(v_j)]_{v_i,v_j\in X}.$$ \end{definition} \begin{definition} The \textbf{support} of $X\subset A$ of the single valued neutrosophic set $A = \{, x\in X\}$: $$supp(X)=\{x\in X:~T_A(x),I_A(x),F_A(x)> 0\}.$$ \end{definition} \begin{definition}(General Forms of Neutrosophic SuperHyperGraph (NSHG)).\\ Assume $V'$ is a given set. A \textbf{neutrosophic SuperHyperGraph} (NSHG) $S$ is an ordered pair $S=(V,E),$ where \begin{itemize} \item[$(i)$] $V=\{V_1,V_2,\ldots,V_n\}$ a finite set of finite single valued neutrosophic subsets of $V';$ \item[$(ii)$] $V=\{(V_i,T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)):~T_{V'}(V_i),I_{V'}(V_i),F_{V'}(V_i)\geq0\},~(i=1,2,\ldots,n);$ \item[$(iii)$] $E=\{E_1,E_2,\ldots,E_{n'}\}$ a finite set of finite single valued neutrosophic subsets of $V;$ \item[$(iv)$] $E=\{(E_{i'},T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})):~T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'})\geq0\},~(i'=1,2,\ldots,n');$ \item[$(v)$] $V_i\neq\emptyset,~(i=1,2,\ldots,n);$ \item[$(vi)$] $E_{i'}\neq\emptyset,~(i'=1,2,\ldots,n');$ \item[$(vii)$] $\sum_{i}supp(V_i)=V,~(i=1,2,\ldots,n);$ \item[$(viii)$] $\sum_{i'}supp(E_{i'})=V,~(i'=1,2,\ldots,n').$ \end{itemize} Here the neutrosophic SuperHyperEdges (NSHE) $E_{j'}$ and the neutrosophic SuperHyperVertices (NSHV) $V_j$ are single valued neutrosophic sets. $T_{V'}(V_i),I_{V'}(V_i),$ and $F_{V'}(V_i)$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership the neutrosophic SuperHyperVertex (NSHV) $V_i$ to the neutrosophic SuperHyperVertex (NSHV) $V.$ $T'_{V}(E_{i'}),T'_{V}(E_{i'}),$ and $T'_{V}(E_{i'})$ denote the degree of truth-membership, the degree of indeterminacy-membership and the degree of falsity-membership of the neutrosophic SuperHyperEdge (NSHE) $E_{i'}$ to the neutrosophic SuperHyperEdge (NSHE) $E.$ Thus, the $ii'$th element of the \textbf{incidence matrix} of neutrosophic SuperHyperGraph (NSHG) are of the form $(V_i,T'_{V}(E_{i'}),I'_{V}(E_{i'}),F'_{V}(E_{i'}))$, the sets V and E are crisp sets.\end{definition} \begin{definition}[Characterization of the Neutrosophic SuperHyperGraph (NSHG)](\textbf{Ref.}\cite{4},Section 4,pp.291-292).\\ Assume a neutrosophic SuperHyperGraph (NSHG) $S$ is an ordered pair $S=(V,E).$ The neutrosophic SuperHyperEdges (NSHE) $E_{i'}$ and the neutrosophic SuperHyperVertices (NSHV) $V_i$ of neutrosophic SuperHyperGraph (NSHG) $S=(V,E)$ could be characterized as follow-up items. \begin{itemize} \item[$(i)$] If $|V_i|=1,$ then $V_i$ is called \textbf{vertex}; \item[$(ii)$] if $|V_i|\geq1,$ then $V_i$ is called \textbf{SuperVertex}; \item[$(iii)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{edge}; \item[$(iv)$] if for all $V_i$s are incident in $E_{i'},$ $|V_i|=1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{HyperEdge}; \item[$(v)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|=2,$ then $E_{i'}$ is called \textbf{SuperEdge}; \item[$(vi)$] if there's a $V_i$ is incident in $E_{i'}$ such that $|V_i|\geq1,$ and $|E_{i'}|\geq2,$ then $E_{i'}$ is called \textbf{SuperHyperEdge}. \end{itemize} \end{definition} This SuperHyperModel is too messy and too dense. Thus there's a need to have some restrictions and conditions on SuperHyperGraph. The special case of this SuperHyperGraph makes the patterns and regularities. \begin{definition} A graph is \textbf{SuperHyperUniform} if it's SuperHyperGraph and the number of elements of SuperHyperEdges are the same. \end{definition} To get more visions on , the some SuperHyperClasses are introduced. It makes to have more understandable. \begin{definition} Assume a neutrosophic SuperHyperGraph. There are some SuperHyperClasses as follows. \begin{itemize} \item[(i).] It's \textbf{neutrosophic SuperHyperPath } if it's only one SuperVertex as intersection amid two given SuperHyperEdges with two exceptions; \item[(ii).] it's \textbf{SuperHyperCycle} if it's only one SuperVertex as intersection amid two given SuperHyperEdges; \item[(iii).] it's \textbf{SuperHyperStar} it's only one SuperVertex as intersection amid all SuperHyperEdges; \item[(iv).] it's \textbf{SuperHyperBipartite} it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming two separate sets, has no SuperHyperEdge in common; \item[(v).] it's \textbf{SuperHyperMultiPartite} it's only one SuperVertex as intersection amid two given SuperHyperEdges and these SuperVertices, forming multi separate sets, has no SuperHyperEdge in common; \item[(vi).] it's \textbf{SuperHyperWheel} if it's only one SuperVertex as intersection amid two given SuperHyperEdges and one SuperVertex has one SuperHyperEdge with any common SuperVertex. \end{itemize} \end{definition} \begin{definition} Let an ordered pair $S=(V,E)$ be a neutrosophic SuperHyperGraph (NSHG) $S.$ Then a sequence of neutrosophic SuperHyperVertices (NSHV) and neutrosophic SuperHyperEdges (NSHE) $$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s$$ is called a \textbf{neutrosophic neutrosophic SuperHyperPath } (NSHP) from neutrosophic SuperHyperVertex (NSHV) $V_1$ to neutrosophic SuperHyperVertex (NSHV) $V_s$ if either of following conditions hold: \begin{itemize} \item[$(i)$] $V_i,V_{i+1}\in E_{i'};$ \item[$(ii)$] there's a vertex $v_i\in V_i$ such that $v_i,V_{i+1}\in E_{i'};$ \item[$(iii)$] there's a SuperVertex $V'_i \in V_i$ such that $V'_i,V_{i+1}\in E_{i'};$ \item[$(iv)$] there's a vertex $v_{i+1}\in V_{i+1}$ such that $V_i,v_{i+1}\in E_{i'};$ \item[$(v)$] there's a SuperVertex $V'_{i+1} \in V_{i+1}$ such that $V_i,V'_{i+1}\in E_{i'};$ \item[$(vi)$] there are a vertex $v_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $v_i,v_{i+1}\in E_{i'};$ \item[$(vii)$] there are a vertex $v_i\in V_i$ and a SuperVertex $V'_{i+1} \in V_{i+1}$ such that $v_i,V'_{i+1}\in E_{i'};$ \item[$(viii)$] there are a SuperVertex $V'_i\in V_i$ and a vertex $v_{i+1}\in V_{i+1}$ such that $V'_i,v_{i+1}\in E_{i'};$ \item[$(ix)$] there are a SuperVertex $V'_i\in V_i$ and a SuperVertex $V'_{i+1} \in V_{i+1}$ such that $V'_i,V'_{i+1}\in E_{i'}.$ \end{itemize} \end{definition} \begin{definition}(Characterization of the Neutrosophic neutrosophic SuperHyperPath s).\\ Assume a neutrosophic SuperHyperGraph (NSHG) $S$ is an ordered pair $S=(V,E).$ A neutrosophic neutrosophic SuperHyperPath (NSHP) from neutrosophic SuperHyperVertex (NSHV) $V_1$ to neutrosophic SuperHyperVertex (NSHV) $V_s$ is sequence of neutrosophic SuperHyperVertices (NSHV) and neutrosophic SuperHyperEdges (NSHE) $$V_1,E_1,V_2,E_2,V_3,\ldots,V_{s-1},E_{s-1},V_s,$$ could be characterized as follow-up items. \begin{itemize} \item[$(i)$] If for all $V_i,E_{j'},$ $|V_i|=1,~|E_{j'}|=2,$ then NSHP is called \textbf{path}; \item[$(ii)$] if for all $E_{j'},$ $|E_{j'}|=2,$ and there's $V_i,$ $|V_i|\geq1,$ then NSHP is called \textbf{SuperPath}; \item[$(iii)$] if for all $V_i,E_{j'},$ $|V_i|=1,~|E_{j'}|\geq2,$ then NSHP is called \textbf{HyperPath}; \item[$(iv)$] if there are $V_i,E_{j'},$ $|V_i|\geq1,|E_{j'}|\geq2,$ then NSHP is called \textbf{neutrosophic SuperHyperPath }. \end{itemize} \end{definition} \begin{definition}((neutrosophic) SuperHyperMatching).\\ Assume a SuperHyperGraph. Then \begin{itemize} \item[$(i)$] a \textbf{neutrosophic SuperHyperMatching} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; \item[$(ii)$] a \textbf{neutrosophic SuperHyperMatching} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; \item[$(iii)$] a \textbf{neutrosophic SuperHyperMatching SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperEdges such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; \item[$(iv)$] a \textbf{neutrosophic SuperHyperMatching SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperEdges such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient; \item[$(v)$] a \textbf{neutrosophic R-SuperHyperMatching} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge; \item[$(vi)$] a \textbf{neutrosophic R-SuperHyperMatching} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge; \item[$(vii)$] a \textbf{neutrosophic R-SuperHyperMatching SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the coefficients defined as the number of the maximum cardinality of a SuperHyperSet $S$ of high cardinality SuperHyperVertices such that there's no SuperHyperVertex not to in a SuperHyperEdge and there's no SuperHyperEdge to have a SuperHyperVertex in a SuperHyperEdge and the power is corresponded to its coefficient; \item[$(viii)$] a \textbf{neutrosophic R-SuperHyperMatching SuperHyperPolynomial} $\mathcal{C}(NSHG)$ for a neutrosophic SuperHyperGraph $NSHG:(V,E)$ is the neutrosophic SuperHyperPolynomial contains the neutrosophic coefficients defined as the neutrosophic number of the maximum neutrosophic cardinality of a neutrosophic SuperHyperSet $S$ of high neutrosophic cardinality neutrosophic SuperHyperVertices such that there's no neutrosophic SuperHyperVertex not to in a neutrosophic SuperHyperEdge and there's no neutrosophic SuperHyperEdge to have a neutrosophic SuperHyperVertex in a neutrosophic SuperHyperEdge and the neutrosophic power is neutrosophicly corresponded to its neutrosophic coefficient. \end{itemize} \end{definition} \begin{definition}((neutrosophic)$\delta-$SuperHyperMatching).\\ Assume a SuperHyperGraph. Then \begin{itemize} \item[$(i)$] an \textbf{$\delta-$SuperHyperMatching} is a \underline{maximal} of SuperHyperVertices with a \underline{maximum} cardinality such that either of the following expressions hold for the (neutrosophic) cardinalities of SuperHyperNeighbors of $s\in S:$ \begin{eqnarray} &&|S\cap N(s)| > |S\cap (V\setminus N(s))|+\delta; \label{119EQN1} \\&& |S\cap N(s)| |S\cap (V\setminus N(s))|_{neutrosophic}+\delta; \label{119EQN3} \\&& |S\cap N(s)|_{neutrosophic} < |S\cap (V\setminus N(s))|_{neutrosophic}+\delta. \label{119EQN4} \end{eqnarray} The Expression \eqref{119EQN3}, holds if $S$ is a \textbf{neutrosophic $\delta-$SuperHyperOffensive}. And the Expression \eqref{119EQN4}, holds if $S$ is a \textbf{neutrosophic $\delta-$SuperHyperDefensive}. \end{itemize} \end{definition} For the sake of having a neutrosophic SuperHyperMatching, there's a need to ``\textbf{redefine}'' the notion of ``neutrosophic SuperHyperGraph''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. \begin{definition}\label{119DEF1} Assume a neutrosophic SuperHyperGraph. It's redefined \textbf{neutrosophic SuperHyperGraph} if the Table \eqref{119TBL3} holds. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{119DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices & The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&The maximum Values of Its Vertices\\ \hline The Values of The Edges&The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{119TBL3} \end{table} \end{definition} It's useful to define a ``neutrosophic'' version of SuperHyperClasses. Since there's more ways to get neutrosophic type-results to make a neutrosophic more understandable. \begin{definition}\label{119DEF2} Assume a neutrosophic SuperHyperGraph. There are some \textbf{neutrosophic SuperHyperClasses} if the Table \eqref{119TBL4} holds. Thus neutrosophic SuperHyperPath , SuperHyperCycle, SuperHyperStar, SuperHyperBipartite, SuperHyperMultiPartite, and SuperHyperWheel, are \textbf{neutrosophic neutrosophic SuperHyperPath }, \textbf{neutrosophic SuperHyperCycle}, \textbf{neutrosophic SuperHyperStar}, \textbf{neutrosophic SuperHyperBipartite}, \textbf{neutrosophic SuperHyperMultiPartite}, and \textbf{neutrosophic SuperHyperWheel} if the Table \eqref{119TBL4} holds. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph, Mentioned in the Definition \eqref{119DEF2}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices & The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&The maximum Values of Its Vertices\\ \hline The Values of The Edges&The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{119TBL4} \end{table} \end{definition} It's useful to define a ``neutrosophic'' version of a SuperHyperMatching. Since there's more ways to get type-results to make a SuperHyperMatching more understandable. \\ For the sake of having a neutrosophic SuperHyperMatching, there's a need to ``\textbf{redefine}'' the notion of `` ''. The SuperHyperVertices and the SuperHyperEdges are assigned by the labels from the letters of the alphabets. In this procedure, there's the usage of the position of labels to assign to the values. \begin{definition}\label{119DEF1} Assume a SuperHyperMatching. It's redefined a \textbf{neutrosophic SuperHyperMatching} if the Table \eqref{119TBL1} holds. \begin{table} \centering \caption{The Values of Vertices, SuperVertices, Edges, HyperEdges, and SuperHyperEdges Belong to The Neutrosophic SuperHyperGraph Mentioned in the Definition \eqref{119DEF1}} \begin{tabular}[t]{c|c} \hline The Values of The Vertices & The Number of Position in Alphabet\\ \hline The Values of The SuperVertices&The maximum Values of Its Vertices\\ \hline The Values of The Edges&The maximum Values of Its Vertices\\ \hline The Values of The HyperEdges&The maximum Values of Its Vertices\\ \hline The Values of The SuperHyperEdges&The maximum Values of Its Endpoints \\ \hline \end{tabular} \label{119TBL1} \end{table} \end{definition} \section{neutrosophic SuperHyperMatching} The SuperHyperNotion, namely, SuperHyperMatching, is up. Thus the non-obvious neutrosophic SuperHyperMatching, $S$ is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: $S$ is the neutrosophic SuperHyperSet, not: $S$ does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only $S$ in a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ with a illustrated SuperHyperModeling. It's also, a neutrosophic free-triangle SuperHyperModel. But all only non-obvious simple neutrosophic type-SuperHyperSets of the neutrosophic SuperHyperMatching amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets, are $S.$ A connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ as Linearly-over-packed SuperHyperModel is featured on the Figures. \begin{example}\label{119EXM1} Assume the SuperHyperGraphs in the Figures \eqref{119NSHG1}, \eqref{119NSHG2}, \eqref{119NSHG3}, \eqref{119NSHG4}, \eqref{119NSHG5}, \eqref{119NSHG6}, \eqref{119NSHG7}, \eqref{119NSHG8}, \eqref{119NSHG9}, \eqref{119NSHG10}, \eqref{119NSHG11}, \eqref{119NSHG12}, \eqref{119NSHG13}, \eqref{119NSHG14}, \eqref{119NSHG15}, \eqref{119NSHG16}, \eqref{119NSHG17}, \eqref{119NSHG18}, \eqref{119NSHG19}, and \eqref{119NSHG20}. \begin{itemize} \item On the Figure \eqref{119NSHG1}, the neutrosophic SuperHyperNotion, namely, neutrosophic SuperHyperMatching, is up. $E_1$ and $E_3$ are some empty neutrosophic SuperHyperEdges but $E_2$ is a loop neutrosophic SuperHyperEdge and $E_4$ is a neutrosophic SuperHyperEdge. Thus in the terms of neutrosophic SuperHyperNeighbor, there's only one neutrosophic SuperHyperEdge, namely, $E_4.$ The neutrosophic SuperHyperVertex, $V_3$ is neutrosophic isolated means that there's no neutrosophic SuperHyperEdge has it as a neutrosophic endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ \underline{\textbf{is}} excluded in every given neutrosophic SuperHyperMatching. \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} \item On the Figure \eqref{119NSHG2}, the SuperHyperNotion, namely, SuperHyperMatching, is up. $E_1$ and $E_3$ SuperHyperMatching are some empty SuperHyperEdges but $E_2$ is a loop SuperHyperEdge and $E_4$ is a SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there's only one SuperHyperEdge, namely, $E_4.$ The SuperHyperVertex, $V_3$ is isolated means that there's no SuperHyperEdge has it as an endpoint. Thus the neutrosophic SuperHyperVertex, $V_3,$ \underline{\textbf{is}} excluded in every given neutrosophic SuperHyperMatching. \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} \item On the Figure \eqref{119NSHG3}, the SuperHyperNotion, namely, SuperHyperMatching, is up. $E_1,E_2$ and $E_3$ are some empty SuperHyperEdges but $E_4$ is a SuperHyperEdge. Thus in the terms of SuperHyperNeighbor, there's only one SuperHyperEdge, namely, $E_4.$ \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^3~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} \item On the Figure \eqref{119NSHG4}, the SuperHyperNotion, namely, a SuperHyperMatching, is up. There's no empty SuperHyperEdge but $E_3$ are a loop SuperHyperEdge on $\{F\},$ and there are some SuperHyperEdges, namely, $E_1$ on $\{H,V_1,V_3\},$ alongside $E_2$ on $\{O,H,V_4,V_3\}$ and $E_4,E_5$ on $\{N,V_1,V_2,V_3,F\}.$ \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} \underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)=\{E_4,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=\{E_5,E_2\}~\text{is an neutrosophic SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=2z^2~\text{is an neutrosophic SuperHyperMatching SuperHyperPolynomial.} \\&& \mathcal{C}(NSHG)=\{V_1,V_2,V_3,V_4\}~\text{is an neutrosophic R-SuperHyperMatching.} \\&& \mathcal{C}(NSHG)=z^4~{\small\text{is an neutrosophic R-SuperHyperMatching SuperHyperPolynomial.}} \end{eqnarray*} \item On the Figure \eqref{119NSHG5}, the SuperHyperNotion, namely, SuperHyperMatching, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{are} only \underline{\textbf{same}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{same}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} Doesn't have less than same SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*}\underline{\textbf{Is}} the obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are only less than same neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} Thus the obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, is: \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} Is the neutrosophic SuperHyperSet, is: \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching}}=\{E_1\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-SuperHyperMatching SuperHyperPolynomial}}=4z^1. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching}}=\{V_1,V_2,V_3,V_4,V_5\}. \\&& \mathcal{C}(NSHG)_{\text{neutrosophic Quasi-R-SuperHyperMatching SuperHyperPolynomial}}=2z^5. \end{eqnarray*} In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ is mentioned as the SuperHyperModel $ESHG:(V,E)$ in the Figure \eqref{119NSHG5}. \item On the Figure \eqref{119NSHG6}, the SuperHyperNotion, namely, SuperHyperMatching, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} \underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=5z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} \item On the Figure \eqref{119NSHG7}, the SuperHyperNotion, namely, SuperHyperMatching, is up. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} \underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=2z^7+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=3z^{14}. \end{eqnarray*} \item On the Figure \eqref{119NSHG8}, the SuperHyperNotion, namely, SuperHyperMatching, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ of dense SuperHyperModel as the Figure \eqref{119NSHG8}. \item On the Figure \eqref{119NSHG9}, the SuperHyperNotion, namely, SuperHyperMatching, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperVertices is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} \underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=12}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=3z^{11}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{22}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{22}. \end{eqnarray*} In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ of highly-embedding-connected SuperHyperModel as the Figure \eqref{119NSHG9}. \item On the Figure \eqref{119NSHG10}, the SuperHyperNotion, namely, SuperHyperMatching, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*}\underline{\textbf{Is}} the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. Since the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is an neutrosophic SuperHyperMatching $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is the neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperVertices such that there's no a neutrosophic SuperHyperEdge for some neutrosophic SuperHyperVertices given by that neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching \underline{\textbf{and}} it's an neutrosophic \underline{\textbf{ SuperHyperMatching}}. Since it\underline{\textbf{'s}} \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There aren't only less than three neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Thus the non-obvious neutrosophic SuperHyperMatching, \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is up. The obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Is the neutrosophic SuperHyperSet, not: \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} Does includes only less than three SuperHyperVertices in a connected neutrosophic SuperHyperGraph $ESHG:(V,E).$ It's interesting to mention that the only non-obvious simple neutrosophic type-SuperHyperSet called the \begin{center} \underline{\textbf{``neutrosophic SuperHyperMatching''}} \end{center} amid those obvious[non-obvious] simple neutrosophic type-SuperHyperSets called the \begin{center} \underline{\textbf{neutrosophic SuperHyperMatching}}, \end{center} is only and only \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_i\}_{i=15}^{17}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=+z^{3}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^{14}. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=z^{14}. \end{eqnarray*} In a connected neutrosophic SuperHyperGraph $ESHG:(V,E)$ of dense SuperHyperModel as the Figure \eqref{119NSHG10}. \item On the Figure \eqref{119NSHG11}, the SuperHyperNotion, namely, SuperHyperMatching, is up. There's neither empty SuperHyperEdge nor loop SuperHyperEdge. The following neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices] is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_1,E_3\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_6,E_7,E_8\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=z^3+z^2. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^6. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=2z^6. \end{eqnarray*} is the simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching. The neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_1,E_3\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_6,E_7,E_8\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=z^3+z^2. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^6. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=2z^6. \end{eqnarray*} Is an \underline{\textbf{neutrosophic SuperHyperMatching}} $\mathcal{C}(ESHG)$ for an neutrosophic SuperHyperGraph $ESHG:(V,E)$ is a neutrosophic type-SuperHyperSet with \underline{\textbf{the maximum neutrosophic cardinality}} of a neutrosophic SuperHyperSet $S$ of neutrosophic SuperHyperEdges[SuperHyperVertices] such that there's no neutrosophic SuperHyperVertex of a neutrosophic SuperHyperEdge is common and there's an neutrosophic SuperHyperEdge for all neutrosophic SuperHyperVertices. There are \underline{not} only \underline{\textbf{two}} neutrosophic SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious neutrosophic SuperHyperMatching is up. The obvious simple neutrosophic type-SuperHyperSet called the neutrosophic SuperHyperMatching is a neutrosophic SuperHyperSet \underline{\textbf{includes}} only \underline{\textbf{two}} neutrosophic SuperHyperVertices. But the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_1,E_3\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_6,E_7,E_8\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=z^3+z^2. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^6. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching SuperHyperPolynomial}=2z^6. \end{eqnarray*} Doesn't have less than three SuperHyperVertices \underline{\textbf{inside}} the intended neutrosophic SuperHyperSet. Thus the non-obvious simple neutrosophic type-SuperHyperSet of the neutrosophic SuperHyperMatching \underline{\textbf{is}} up. To sum them up, the neutrosophic SuperHyperSet of the neutrosophic SuperHyperEdges[SuperHyperVertices], \begin{eqnarray*} && \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_1,E_3\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching}=\{E_6,E_7,E_8\}. \\&& \mathcal{C}(NSHG)_{neutrosophic SuperHyperMatching SuperHyperPolynomial}=z^3+z^2. \\&& \mathcal{C}(NSHG)_{neutrosophic R-SuperHyperMatching}=\{V_i\}_{i=1}^6. \\&& \mathc