COMPUTATION OF TOPOLOGICAL INDICES OF NON-COMMUTING GRAPHS

Abstract

Let G be a non-abelian finite group.  The non-commuting graph Γ_G of G is defined as a graph with vertex set G − Z(G) in which two distinct vertices x and y are joined if and only if xy ≠ yx.  Various topological indices have been defined for simple and connected graphs.  Since non-commuting graph is a simple and connected graph, topological indices could be defined for it.  The main object of this article is to calculate various indices like Wiener index, Hyper-Wiener index, Schultz index and Gutman index for the non-commuting graph of the group G.