Common neighborhood (signless) Laplacian spectrum and energy of CCC-graph

In this paper, we consider commuting conjugacy class graph (abbreviated as CCC-graph) of a finite group G which is a graph with vertex set : x ∈ G Z(G)\ (where xG denotes the conjugacy class containing x) and two distinct vertices xG and yG are joined by an edge if there exist some elements x'∈ xG and y'∈ yG such that they commute. We compute common neighborhood (signless) Laplacian spectrum and energy of CCC-graph of finite non-abelian groups whose central quotient is isomorphic to either Zₚ × Zₚ (where p is any prime) or the dihedral group D₂ₙ (n ≥ 3); and determine whether CCC-graphs of these groups are common neighborhood (signless) Laplacian hyperenergetic/borderenergetic. As a consequence, we characterize certain finite non-abelian groups viz. D₂ₙ, T₄ₙ, U₆ₙ, U(n, m), SD₈ₙ and V₈ₙ such that their CCC-graphs are common neighborhood (signless) Laplacian hyperenergetic/borderenergetic.