Laplacian Spectrum of Non-Commuting Graphs of Finite Groups

Abstract

In this paper, we compute Laplacian energy of the non-commuting graphs of some classes of finite non-abelian groups.

Spectrum and energies of commuting conjugacy class graph of a finite group

“…In this paper we compute spectrum, Laplacian spectrum, signless Laplacian spectrum and their corresponding energies (i.e., energy Laplacian energy and signless Laplacian energy) of commuting conjugacy class graph of G(p, m, n). As a consequence we see that CCC(G) is super integral [4,9] if G = G(p, m, n). Also, it satisfies E-LE Conjecture of Gutman et al [1,8].…”

Energy of commuting graph of finite AC-groups

“…It may be mentioned here that E(K n ) = 2n − 2, where K n is the complete graph on n vertices. Spectral aspects of Γ G are considered in [6], [7], [8], [9], [10] and [18] recently for various families of finite groups. In this paper we compute energy of Γ G for several classes of finite AC-groups and discuss some consequences regarding hyperenergetic and borderenergetic graphs.…”

Common Neighborhood Energy of Commuting Graphs of Finite Groups

“…We write Γ c (G) to denote this graph. In [16][17][18][19][20][21][22][23], various aspects of Γ c (G) are studied. In Section 2 of this paper, we derive an expression for computing CN-energy of a particular class of graphs and list a few already known results.…”