Energy of commuting graph of finite groups whose centralizers are Abelian

Reza Sharafdini, Rezvan Darbandi

Published 2017-04-21Version 1

Let $G$ be a finite group with centre $Z(G)$. The commuting graph of a non-Abelian group $G$, denoted by $\Gamma_G$, is a simple undirected graph whose vertex set is $G\setminus Z(G)$, and two vertices $x$ and $y$ are adjacent if and only if $xy = yx$. In this article we aim to compute the ordinary energy of $\Gamma_G$ for groups $G$ whose centralizers are Abelian.