Spectral aspects of commuting conjugacy class graph of finite groups

The commuting conjugacy class graph of a non-abelian group G, denoted by \mathcal{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 x^G and y^G are adjacent if there exists some elements x' \in x^G and y' \in y^G such that x'y' = y'x'. In this paper we compute various spectra and energies of commuting conjugacy class graph of the groups D_{۲n}, Q_{۴m}, U_{(n, m)}, V_{۸n} and SD_{۸n}. Our computation shows that \mathcal{CCC}(G) is super integral for these groups. We compare various energies and as a consequence it is observed that \mathcal{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 \mathcal{CCC}(G) is hyperenergetic, L-hyperenergetic or Q-hyperenergetic.

کلیدواژه ها:

Commuting conjugacy class graph ، spectrum ، Energy ، Finite group