Non-Commuting Graphs of Nilpotent Groups

Abstract

Let G be a non-abelian group and Z(G) be the center of G. The non-commuting graph ΓG associated to G is the graph whose vertex set is G{set minus}Z(G) and two distinct elements x, y are adjacent if and only if xy ≠ yx. We prove that if G and H are non-abelian nilpotent groups with irregular isomorphic non-commuting graphs, then {pipe}G{pipe} = {pipe}H{pipe}. © 2014 Copyright Taylor & Francis Group, LLC.