On the distance & distance (signless) Laplacian spectra of non-commuting graphs

Abstract

Let $Z(G)$ be the centre of a finite non-abelian group $G.$ The non-commuting graph of $G$ is a simple undirected graph with vertex set $G\setminus Z(G),$ and two vertices $u$ and $v$ are adjacent if and only if $uv\ne vu.$ In this paper, we investigate the distance, distance (signless) Laplacian spectra of non-commuting graphs of some classes of finite non-abelian groups, and obtain some conditions on a group so that the non-commuting graph is distance, distance (signless) Laplacian integral.