Common neighborhood spectrum of commuting graphs of finite groups

Abstract

The commuting graph of a finite non-abelian group G with center Z(G), denoted by Гc(G), is a simple undirected graph whose vertex set is G\ Z(G), and two distinct vertices x and y are adjacent if and only if xy = yx. In this paper, we compute the common neighborhood spectrum of commuting graphs of several classes of finite non-abelian groups and conclude that these graphs are CN-integral.