  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.
