Common neighbourhood spectrum and energy of commuting conjugacy class graph

Abstract

In this paper we compute common neighbourhood (abbreviated as CN) spectrum and energy of commuting conjugacy class graph of several families of finite non-abelian groups. As a consequence of our results we show that the commuting conjugacy class graphs of the groups $D_{2n}$, $T_{4n}$, $S{D}_{8n}$, $U_{(n,m)}$, $U_{6n}$, $V_{8n}$, $G(p,m,n)$ and some families of groups whose central quotient is isomorphic to $D_{2n}$ or $Z_p\times Z_p$, for some prime $p$, are CN-integral but not CN-hyperenergetic.

20 pages