Spectrum and energies of a graph

Abstract

In this paper, we compute spectrum, Laplacian spectrum, signless Laplacian spectrum and their corresponding energies of commuting conjugacy class graph of the non-abelian p-group of order p n whose order of the centre is pⁿ⁻², p is prime and n ≥ 3. We derive some consequences along with the fact that commuting conjugacy class graph of the above group is super integral. We also compare various energies and determine whether commuting conjugacy class graph of the group is hyperenergetic, L-hyperenergetic or Q-hyperenergetic. We compute the genus of the graph. Finally we conclude the paper by noting the fact that the graph is neither toroidal nor double-toroidal nor triple-toroidal.