Characterization of SL(2, q) by its non-commuting graph

Abstract

Let G be a non-abelian group and Z(G) be its center. The non-commuting graph AG of G is the graph whose vertex set is G\Z(G) and two vertices are joined by an edge if they do not commute. Let SL(2,q) be the special linear group of degree 2 over the finite field of order q. In this paper we prove that if G is a group such that AG ≅ ASL(2,q) for some prime power q ≥ 2, then G ≅ SL(2,q). © 2009 Heldermann Verlag.