SPECTRAL ASPECTS OF COMMUTING CONJUGACY CLASS GRAPH OF FINITE GROUPS

The commuting conjugacy class graph of a non-abelian group G, denoted by CCC(G), is a simple undirected graph whose vertex set is the set of conjugacy classes of the non-central elements of G and two distinct vertices xG and yG are adjacent if there exists some elements x ′ 2 xG and y ′ 2 yG such that x ′ y ′ = y ′ x ′ . In this paper we compute various spectra and energies of commuting conjugacy class graph of the groups D2n;Q4m;U(n;m); V8n and SD8n. Our computation shows that CCC(G) is super integral for these groups. We compare various energies and as a consequence it is observed that CCC(G) satisfy E-LE Conjecture of Gutman et al. We also provide negative answer to a question posed by Dutta et al. comparing Laplacian and Signless Laplacian energy. Finally, we conclude this paper by characterizing the above mentioned groups G such that CCC(G) is hyperenergetic, L-hyperenergetic or Q- hyperenergetic.