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

Kalita, Jharna (Tezpur University)
Paul, Somnath (Tezpur University)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 13, No 2 (2025): Electronic Journal of Graph Theory and Applications

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.