On Some Topological Indices Defined via the Modified Sombor Matrix期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On Some Topological Indices Defined via the Modified Sombor Matrix

Authors:	Xuewu Zuo Bilal Ahmad Rather Muhammad Imran Akbar Ali

Affiliation:	1.Department of Common Course, Anhui Xinhua University, Hefei 230088, China;2.Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al Ain, Abu Dhabi 15551, United Arab Emirates;3.Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il P.O. Box 2240, Saudi Arabia

Abstract:	Let G be a simple graph with the vertex set $V = {v_{1}, \dots, v_{n}}$ and denote by $d_{v_{i}}$ the degree of the vertex $v_{i}$ . The modified Sombor index of G is the addition of the numbers ${(d_{v_{i}}^{2} + d_{v_{j}}^{2})}^{- 1 / 2}$ over all of the edges $v_{i} v_{j}$ of G. The modified Sombor matrix $A_{M S} (G)$ of G is the n by n matrix such that its $(i, j)$ -entry is equal to ${(d_{v_{i}}^{2} + d_{v_{j}}^{2})}^{- 1 / 2}$ when $v_{i}$ and $v_{j}$ are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of $A_{M S} (G)$ . The sum of the absolute eigenvalues of $A_{M S} (G)$ is known as the modified Sombor energy of G. Two graphs with the same modified Sombor energy are referred to as modified Sombor equienergetic graphs. In this article, several bounds for the modified Sombor index, the modified Sombor spectral radius, and the modified Sombor energy are found, and the corresponding extremal graphs are characterized. By using computer programs (Mathematica and AutographiX), it is found that there exists only one pair of the modified Sombor equienergetic chemical graphs of an order of at most seven. It is proven that the modified Sombor energy of every regular, complete multipartite graph is $\sqrt{2}$ ; this result gives a large class of the modified Sombor equienergetic graphs. The (linear, logarithmic, and quadratic) regression analyses of the modified Sombor index and the modified Sombor energy together with their classical versions are also performed for the boiling points of the chemical graphs of an order of at most seven.

Keywords:	adjacency matrix Sombor index modified Sombor matrix modified Sombor energy correlation

设为首页 | 免责声明 | 关于勤云 | 加入收藏