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Let $G$ be a finite non abelian group. The centralizer graph of $G$ is asimple undirected graph $\Gamma_{cent}(G)$, whose vertices are the propercentralizers of $G$ and two vertices are adjacent if and only if theircardinalities are identical {\rm\cite{omer}}. The complement of the centralizergraph is called the co-centralizer graph. In this paper, we investigate theadjacency and (signless) Laplacian spectra of centralizer and co-centralizergraphs of some classes of finite non-abelian groups and obtain some conditionson a group so that the centralizer and co-centralizer graphs are adjacency,(signless) Laplacian integral.

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