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arXiv · 2208.01042

A note on the distance spectra of co-centralizer graphs

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 vertex set consists of proper centralizers of $G$ and two vertices are adjacent if and only if their cardinalities are identical [6]. We call the complement of the centralizer graph as the co-centralizer graph. In this paper, we investigate the distance, distance (signless) Laplacian spectra of co-centralizer graphs of some classes of finite non-abelian groups, and obtain some conditions on a group so that the co-centralizer graph is distance, distance (signless) Laplacian integral.

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Jharna Kalita, Somnath Paul. 2022-08-01. A note on the distance spectra of co-centralizer graphs. https://arxiv.org/abs/2208.01042

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