Spectrum and energies of commuting conjugacy class graph of a finite group

Abstract

In this paper we compute spectrum, Laplacian spectrum, signless Laplacian spectrum and their corresponding energies of commuting conjugacy class graph of the group $G(p,m,n)=⟨x,y:x^{p^m}=y^{p^n}=[x,y{]}^p=1,[x,[x,y]]=[y,[x,y]]=1⟩$, where $p$ is any prime, $m\ge 1$ and $n\ge 1$. We derive some consequences along with the fact that commuting conjugacy class graph of $G(p,m,n)$ is super integral. We also compare various energies and determine whether commuting conjugacy class graph of $G(p,m,n)$ is hyperenergetic, L-hyperenergetic or Q-hyperenergetic.

13 pages