Various spectral aspects of NCCC-graphs of certain finite non-abelian groups

2025/08/27 by Chakraborty, Rishabh, Jannat, Firdous Ee, Nath, Rajat Kanti
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2508.19616

Abstract

Let G be a finite non-abelian group. The non-commuting conjugacy class graph (abbreviated as NCCC-graph) of G is a simple undirected graph whose vertex set is the set of conjugacy classes of non-central elements of G and two vertices x^G and y^G are adjacent to each other if x' and y' does not commute for all x'∈ x^G and y'∈ y^G, where x^G is the conjugacy class of x ∈ G. In this paper, we compute the spectrum, Laplacian spectrum, signless Laplacian spectrum and corresponding energies of NCCC-graphs of certain families of finite non-abelian groups. We determine whether these graphs are integral, L-integral and Q-integral. Further, we compare energy, Laplacian energy and signless Laplacian energy; and determine whether these graphs are borderenergetic, L-borderenergetic, Q-borderenergetic, hyperenergetic, L-hyperenergetic or Q-hyperenergetic.

Citations

• A survey on conjugacy class graphs of groups
• Signless Laplacian energies of non-commuting graphs of finite groups and related results
• Common neighbourhood spectrum and energy of commuting conjugacy class graph
• Spectrum and energies of commuting conjugacy class graph of a finite\n group
• Spectral aspects of commuting conjugacy class graph of finite groups
• L-Borderenergetic graphs
• The Laplacian Spectrum of a Graph II

Related

• Spectral aspects of commuting conjugacy class graph of finite groups
• Common neighborhood (signless) Laplacian spectrum and energy of CCC-graph
• Spectrum and energy of non-commuting graphs of finite groups
• Common neighborhood Laplacian and signless Laplacian spectra and energies of commuting graphs
• Signless Laplacian energies of non-commuting graphs of finite groups and related results