2024/11/23 by Varun J Kaushik, Kaushik, Varun J, Ekta +3
Mathematics · #05C25 #05C50 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Group Theory (math.GR) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2411.16734
openalex publication_date 2024/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a graph A on a group G and an equivalence relation B on G, the B superA graph, whose vertex set is G and two vertices g, h are adjacent if and only if there exist g′ ∈[g] and h′ ∈[h] such that g′ and h′ are adjacent in A. Recently, Dalal et al. (Spectrum of super commuting graphs of some finite groups, Computational and Applied Mathematics, 43(6):348, 2024) obtain the Laplacian spectrum of supercommuting graphs of certain non-abelian groups including the dihedral group and the generalized quaternion group. In this paper, we continue the study of Laplacian spectrum of certian B superA graphs. We obtain the Laplacian spectrum of conjugacy superenhanced power graphs of certain non-abelian groups, namely: dihedral group, generalized quaternion group and semidihedral group. Moreover to enhance the work of Dalal et al, we obtain the Laplacian spectrum of conjugacy supercommuting graph of semidihedral group. We prove that graphs considered in this paper are L-integral.