On Some Topological Indices Defined via the Modified Sombor Matrix

Abstract

Let G be a simple graph with the vertex set V={v1,…,vn} and denote by dvi the degree of the vertex vi. The modified Sombor index of G is the addition of the numbers (dvi2+dvj2)−1/2 over all of the edges vivj of G. The modified Sombor matrix AMS(G) of G is the n by n matrix such that its (i,j)-entry is equal to (dvi2+dvj2)−1/2 when vi and vj are adjacent and 0 otherwise. The modified Sombor spectral radius of G is the largest number among all of the eigenvalues of AMS(G). The sum of the absolute eigenvalues of AMS(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 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.

The Effect of Vertex and Edge Removal on Sombor Index

“…Also in [22], the Sombor index was used to predict physicochemical properties of butane derivatives. After defining the Sombor index, its modified version was put forward in [23] and studied in [24][25][26][27].…”

Analysis of a Productive Topological Index Correlated to Fullerenes’ Physical Properties

“…For the famous COVID-19 drug Remdesivir, the reverse general Randic index, reverse atom bond connectivity index, reverse geometric arithmetic index, reverse forgotten index, reverse Balaban index, and other types of Zagreb indices are computed to help in the development of new corona virus treatment [25]. The modified Sombor index and modified Sombor energy give a better quadratic correlation than their corresponding classical versions with the boiling points of the chemical graphs of the order of at most seven [26].…”