  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.
