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Numerous graph energies of regular subdivision graph and complete graph

العديد من طاقات الرسم البياني للرسم البياني العادي للتقسيم الفرعي والرسم البياني الكامل
Authors: Imrana Kousar; Saima Nazeer; Abid Mahboob; Sana Shahid; Yu-Pei Lv;

Numerous graph energies of regular subdivision graph and complete graph

Abstract

L'énergie graphique $ E(G) $ d' un graphique simple $ G $ est la somme de ses valeurs propres absolues où les valeurs propres de la matrice d'adjacence $ A(G) $ sont appelées valeurs propres du graphique $ G $ . Dépend des valeurs propres de différentes matrices de graphe, plusieurs énergies de graphe ont été observées récemment telles que l'énergie de degré maximum, l'énergie Randi$ \acute{c} $ , l'énergie de somme-connectivité, etc. En fonction de la définition d'une matrice graphique, l'énergie du graphique peut être facilement déterminée. Cet article contient les limites supérieures de plusieurs énergies de graphique de $ s $-graphe de subdivision régulier $ S(G) $ . Diverses énergies de graphe du graphe complet sont également mentionnées dans cet article.

La energía del gráfico $ E(G) $ de un gráfico simple $ G $ es la suma de sus valores propios absolutos, donde los valores propios de la matriz de adyacencia $ A(G) $ se denominan valores propios del gráfico $ G $. Depende de los valores propios de diferentes matrices gráficas, recientemente se han observado varias energías gráficas, como la energía de grado máximo, la energía de Randi$ \acute{c} $, la energía de suma-conectividad, etc. Dependiendo de la definición de una matriz gráfica, la energía gráfica se puede determinar fácilmente. Este artículo contiene los límites superiores de varias energías de gráfico de $ s $ -gráfico de subdivisión regular $ S(G) $. También se mencionan varias energías gráficas de gráfico completo en este artículo.

The graph energy $ E(G) $ of a simple graph $ G $ is sum of its absolute eigenvalues where eigenvalues of adjacency matrix $ A(G) $ are referred as eigenvalues of graph $ G $. Depends upon eigenvalues of different graph matrices, several graph energies has been observed recently such as maximum degree energy, Randi$ \acute{c} $ energy, sum-connectivity energy etc. Depending on the definition of a graph matrix, the graph energy can be easily determined. This article contains upper bounds of several graph energies of $ s $-regular subdivision graph $ S(G) $. Also various graph energies of complete graph are mentioned in this article.

طاقة الرسم البياني $ E(G )$ للرسم البياني البسيط $ G $ هي مجموع قيمه الذاتية المطلقة حيث يشار إلى القيم الذاتية للمصفوفة المجاورة $ A(G )$ بالقيم الذاتية للرسم البياني $ G $. اعتمادًا على القيم الذاتية لمصفوفات الرسم البياني المختلفة، لوحظت العديد من طاقات الرسم البياني مؤخرًا مثل طاقة الدرجة القصوى وطاقة راندي$\acute{c }$ وطاقة مجموع الاتصال وما إلى ذلك. اعتمادًا على تعريف مصفوفة الرسم البياني، يمكن تحديد طاقة الرسم البياني بسهولة. تحتوي هذه المقالة على الحدود العليا للعديد من طاقات الرسم البياني $ s $- التقسيم الفرعي المنتظم $ S(G )$. كما تم ذكر طاقات الرسم البياني المختلفة للرسم البياني الكامل في هذه المقالة.

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Keywords

randić index, Materials Science, Integral graph, Zagreb index, Graph, Graph energy, zagreb index, FOS: Chemical sciences, Complement graph, Regular graph, QA1-939, FOS: Mathematics, Materials Chemistry, graph matrices, Cubic graph, Quartic graph, Randić index, Graphene: Properties, Synthesis, and Applications, Null graph, Graph power, graph energy, Graphs and linear algebra (matrices, eigenvalues, etc.), Adjacency matrix, Butterfly graph, Graph Spectra and Topological Indices, Aromaticity in Organic Molecules and Materials, Organic Chemistry, Line graph, Voltage graph, Eigenvalues, graph, Distance-regular graph, Discrete mathematics, Chemistry, Combinatorics, Physical Sciences, Geometry and Topology, Mathematics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
Average
Average
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