On the spectra of non-commuting graphs of certain class of groups

Abstract

Let [Formula: see text] be the center of a finite non-abelian group [Formula: see text] The non-commuting graph of [Formula: see text] is a simple undirected graph with vertex set [Formula: see text] and two vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] A group [Formula: see text] is called a CA-group if the centralizer [Formula: see text] for every non central element [Formula: see text] is abelian. In this paper, we investigate the distance, distance (signless) Laplacian spectra of non-commuting graphs of some CA-groups, and obtain some conditions on them so that the corresponding non-commuting graph is distance, distance (signless) Laplacian integral.