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 \(\Gamma_c(G)\), is a simple undirected graph whose vertex set is \(G\setminus Z(G)\), 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.