On the spectral property of commuting graph of finite groups whose centralizers are Abelian

Let G be a finite group with the centre Z(G). Th e commuting graph of a non-Abelian group G, denoted by ΓG, is a simple undirected graph whose vertex set is G \ Z(G), and two vertices x and y are adjacent if and only if xy = yx. In this article we aim to study spectral property of ΓG for groups whose centralizers are Abelian. We also compute the ordinary and the distance energy of these graphs.