COMMON NEIGHBOURHOOD SPECTRUM AND ENERGY OF COMMUTING CONJUGACY CLASS GRAPH

In this paper, we compute the common neighbourhood (abbreviated as CN) spectrum and the common neighbourhood 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_{۲n}, T_{۴n}, SD_{۸n}, U_{(n,m)}, U_{۶n}, V_{۸n}, G(p, m, n) and some families of groups whose central quotient is isomorphic to D_{۲n} or \mathbb{Z}_p \times \mathbb{Z}_p, for some prime p, are CN-integral but not CN-hyperenergetic.

Keywords:

Common neighborhood , spectrum , Energy , Conjugacy class graph