In this book, some notions are introduced about “Neutrosophic Joint Set”. Two chapters are devised as “Initial Notions”, and “Modified Notions’.’ Two manuscripts are cited as the references of these chapters which are my 81st, and 82nd manuscripts. I’ve used my 81st, and 82nd manuscripts to write this book. In first chapter, there are some points as follow. New setting is introduced to study joint-dominating number and neutrosophic joint-dominating number arising from joint-dominated vertices in neutrosophic graphs assigned to neutrosophic graphs. Minimum number of joint-dominated vertices, is a number which is representative based on those vertices. Minimum neutrosophic number of joint-dominated vertices corresponded to joint-dominating set is called neutrosophic joint-dominating number. Forming sets from joint-dominated vertices to figure out different types of number of vertices in the sets from joint- dominated sets in the terms of minimum number of vertices to get minimum number to assign to neutrosophic graphs is key type of approach to have these notions namely joint-dominating number and neutrosophic joint-dominating number arising from joint-dominated vertices in neutrosophic graphs assigned to neutrosophic graphs. Two numbers and one set are assigned to a neutrosophic graph, are obtained but now both settings lead to approach is on demand which is to compute and to find representatives of sets having smallest number of joint-dominated vertices from different types of sets in the terms of minimum number and minimum neutrosophic number forming it to get minimum number to assign to a neutrosophic graph. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then for given vertex n if sn ∈ E, then s joint-dominates n. Let S be a set of neutrosophic vertices [a vertex alongside triple pair of its values is called neutrosophic vertex.]. If for every neutrosophic vertex n in V \ S, there’s at least one neutrosophic vertex s in S such that s joint-dominates n, then the set of neutrosophic vertices, S is called joint-dominating set where for every two vertices in S, there’s a path in S amid them. The minimum cardinality between all joint-dominating sets is called joint-dominating number and it’s denoted by J(NTG); for given vertex n if sn ∈ E, then s joint-dominates n. Let S be a set of neutrosophic vertices [a vertex alongside triple pair of its values is called neutrosophic vertex.]. If for every neutrosophic vertex n in V \ S, there’s at least one neutrosophic vertex s in S such that s joint-dominates n, then the set of neutrosophic vertices, S is called joint-dominating set where for every two vertices in S, there’s a path in S amid them. The minimum neutrosophic cardinality between all joint-dominating sets is called neutrosophic joint- dominating number and it’s denoted by Jn(NTG). As concluding results, there i Abstract are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path-neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete- bipartite-neutrosophic graphs, complete-t-partite-neutrosophic graphs, and wheel-neutrosophic graphs. The clarifications are also presented in both sections “Setting of joint-dominating number,” and “Setting of neutrosophic joint-dominating number,” for introduced results and used classes. This approach facilitates identifying sets which form joint-dominating number and neutrosophic joint-dominating number arising from joint-dominated vertices in neutrosophic graphs assigned to neutrosophic graphs. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. The cardinality of set of joint-dominated vertices and neutrosophic cardinality of set of joint-dominated vertices corresponded to joint-dominating set have eligibility to define joint- dominating number and neutrosophic joint-dominating number but different types of set of joint-dominated vertices to define joint-dominating sets. Some results get more frameworks and perspective about these definitions. The way in that, different types of set of joint-dominated vertices in the terms of minimum number to assign to neutrosophic graphs, opens the way to do some approaches. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Neutrosophic joint- dominating notion is applied to different settings and classes of neutrosophic graphs. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this chapter. In second chapter, there are some points as follow. New setting is introduced to study joint-resolving number and neutrosophic joint-resolving number arising from joint-resolved vertices in neutrosophic graphs assigned to neutrosophic graphs. Minimum number of joint-resolved vertices, is a number which is representative based on those vertices. Minimum neutrosophic number of joint-resolved vertices corresponded to joint-resolving set is called neutrosophic joint-resolving number. Forming sets from joint-resolved vertices to figure out different types of number of vertices in the sets from joint-resolved sets in the terms of minimum number of vertices to get minimum number to assign to neutrosophic graphs is key type of approach to have these notions namely joint-resolving number and neutrosophic joint-resolving number arising from joint-resolved vertices in neutrosophic graphs assigned to neutrosophic graphs. Two numbers and one set are assigned to a neutrosophic graph, are obtained but now both settings lead to approach is on demand which is to compute and to find representatives of sets having smallest number of joint-resolved vertices from different types of sets in the terms of minimum number and minimum neutrosophic number forming it to get minimum number to assign to a neutrosophic graph. Let NTG : (V,E,σ,μ) be a neutrosophic graph. Then for given two vertices n and n′ , if d(s, n) ̸= d(s, n′ ), then s joint-resolves n and n′ where d is the minimum number of edges amid all paths from the vertex and the another vertex. Let S be a set of neutrosophic vertices [a vertex alongside triple pair of its values is called neutrosophic vertex.]. If for every neutrosophic vertex n in V \ S, there’s at least one neutrosophic vertex s in S such that s joint-resolves n and n′, then the set of neutrosophic vertices, S is called joint-resolving set where for every two vertices in S, there’s a path ii in S amid them. The minimum cardinality between all joint-resolving sets is called joint-resolving number and it’s denoted by J(NTG); for given two vertices n and n′, if d(s,n) ̸= d(s,n′), then s joint-resolves n and n′ where d is the minimum number of edges amid all paths from the vertex and the another vertex. Let S be a set of neutrosophic vertices [a vertex alongside triple pair of its values is called neutrosophic vertex.]. If for every neutrosophic vertices n and n′ in V \ S, there’s at least one neutrosophic vertex s in S such that s joint-resolves n and n′, then the set of neutrosophic vertices, S is called joint-resolving set where for every two vertices in S, there’s a path in S amid them. The minimum neutrosophic cardinality between all joint- resolving sets is called neutrosophic joint-resolving number and it’s denoted by Jn(NTG). As concluding results, there are some statements, remarks, examples and clarifications about some classes of neutrosophic graphs namely path- neutrosophic graphs, cycle-neutrosophic graphs, complete-neutrosophic graphs, star-neutrosophic graphs, complete-bipartite-neutrosophic graphs, complete-t- partite-neutrosophic graphs, and wheel-neutrosophic graphs. The clarifications are also presented in both sections “Setting of joint-resolving number,” and “Setting of neutrosophic joint-resolving number,” for introduced results and used classes. This approach facilitates identifying sets which form joint-resolving number and neutrosophic joint-resolving number arising from joint-resolved vertices in neutrosophic graphs assigned to neutrosophic graphs. In both settings, some classes of well-known neutrosophic graphs are studied. Some clarifications for each result and each definition are provided. The cardinality of set of joint-resolved vertices and neutrosophic cardinality of set of joint- resolved vertices corresponded to joint-resolving set have eligibility to define joint-resolving number and neutrosophic joint-resolving number but different types of set of joint-resolved vertices to define joint-resolving sets. Some results get more frameworks and more perspectives about these definitions. The way in that, different types of set of joint-resolved vertices in the terms of minimum number to assign to neutrosophic graphs, opens the way to do some approaches. These notions are applied into neutrosophic graphs as individuals but not family of them as drawbacks for these notions. Finding special neutrosophic graphs which are well-known, is an open way to pursue this study. Neutrosophic joint-resolving notion is applied to different settings and classes of neutrosophic graphs. Some problems are proposed to pursue this study. Basic familiarities with graph theory and neutrosophic graph theory are proposed for this chapter. [Ref1] Henry Garrett, “Repetitive Joint-Sets Featuring Multiple Numbers For Neutrosophic Graphs”, ResearchGate 2022 (doi: 10.13140/RG.2.2.15113.93283). [Ref2] Henry Garrett, “Separate Joint-Sets Representing Separate Numbers Where Classes of Neutrosophic Graphs and Applications are Cases of Study”, ResearchGate 2022 (doi: 10.13140/RG.2.2.22666.95686). Two chapters are devised as “Initial Notions”, and “Modified Notions’.