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arXiv · 2209.07114

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

Jharna Kalita·Somnath Paul
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Abstract

Let $G$ be a finite non abelian group. The centralizer graph of $G$ is a simple undirected graph $\Gamma_{cent}(G)$, whose vertices are the proper centralizers of $G$ and two vertices are adjacent if and only if their cardinalities are identical {\rm\cite{omer}}. 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.

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Jharna Kalita, Somnath Paul. 2022-09-15. On adjacency and (signless) Laplacian spectra of centralizer and co-centralizer graphs of some finite non-abelian groups. https://arxiv.org/abs/2209.07114

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