The topological indices of non-commuting graph of a finite group

Abstract

Assume G is a non-abelian finite group. The non-commuting graph GG of G is defined as a graph with vertex set G - Z(G) in which Z(G) is the center of G and two distinct vertices x and y are joined if and only if xy ? yx. Various topological indices have been determined for simple and connected graphs. Since non-commuting graph is a simple and connected graph, topological indices could be defined for it. The main objective of this article is to calculate various topological indices including the Szeged index, Edge-Wiener index, the first Zagreb index and the second Zagreb index for the non-commuting graph of G.