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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Kalita, Jharna
Tezpur University
Electrical & Electronics Engineering

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On adjacency and (signless) Laplacian spectra of centralizer and co-centralizer graphs of some finite non-abelian groups Kalita, Jharna; Paul, Somnath
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2025.13.2.12

Abstract

Let G be a finite non-abelian group. The centralizer graph of G is a simple undirected graph Γcent(G), whose vertices are the proper centralizers of G and two vertices are adjacent if and only if their cardinalities are identical. The complement of the centralizer graph is called the co-centralizer graph. In this paper, we investigate the adjacency and (signless) Laplacian spectra of centralizer and co-centralizer graphs of some classes of finite non-abelian groups and obtain some conditions on a group so that the centralizer and co-centralizer graphs are adjacency, (signless) Laplacian integral. We also demonstrate how the integrality phenomena of these graphs either align with or differ from those of the commuting and non-commuting graphs of the corresponding groups.
Co-Authors Paul, Somnath