On adjacency and (signless) Laplacian spectra of centralizer and co-centralizer graphs of some finite non-abelian groups

Jharna Kalita, Somnath Paul

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.

Keywords


Centralizer graph, Co-centralizer graph, Adjacency matrix, Laplacian matrix, signless Laplacian matrix, spectrum, integral graphs.

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DOI: http://dx.doi.org/10.5614/ejgta.2025.13.2.12

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