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 $D_{ 2n}, Q_{ 4m}, U_{ (n, m)}, V_{ 8n}$ and $SD_{ 8n}$. 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.
Categories: math.GR