A characterization of the groups PSU/(4,4) and PSL(4, 4) by non-commuting graph

Abstract

Let G be a finite non-abelian group. We define a graph Γ_G, called the non-commuting graph of G, with vertex set G - Z(G) such that two vertices x and y are adjacent if and only if xy yx. In this paper we prove that if G denotes one of the groups PSU(A, 4) or PSL(4, 4), then for any finite group H, the graph isomorphism Γ_G Γ _H implies H G.