In this paper we compute common neighbourhood (abbreviated as CN) spectrum and energy of commuting conjugacy class graph of several families of finite non-abelian groups. As a consequence of our results we show that the commuting conjugacy class graphs of the groups $D_{ 2n}$, $T_{ 4n}$, $SD_{ 8n}$, $U_{ (n,m)}$, $U_{ 6n}$, $V_{ 8n}$, $G(p, m, n)$ and some families of groups whose central quotient is isomorphic to $D_{ 2n}$ or $Z_p \times Z_p$, for some prime $p$, are CN-integral but not CN-hyperenergetic.
Categories: math.GR