Common neighborhood Laplacian and signless Laplacian spectra and energies of commuting graphs

Abstract

In this paper, we compute common neighbourhood Laplacian spectrum, common neighbourhood signless Laplacian spectrum and their respective energies of commuting graph of some finite non-abelian groups including some AC-groups, groups whose central quotients are isomorphic to $Sz(2)$, $\mathbb{Z}_p\times \mathbb{Z}_p$ or $D_{2m}$. Our findings lead us to conclude that these graphs are CNL (CNSL)-integral. Additionally, we characterize the aforementioned groups such that their commuting graphs are CNL (CNSL)-hyperenergetic.