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

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) = \langle x, y : x^{p^m} = y^{p^n} = [x, y]^p = ۱, [x, [x, y]] = [y, [x, y]] = ۱\rangle, where p is any prime, m \geq ۱ and n \geq ۱. 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.

کلیدواژه ها:

Commuting conjugacy class graph ، Energy ، Finite group ، spectrum