An efficient g-centroid location algorithm for cographs

In 1998, Pandu Rangan et al. proved that locating the g-centroid for an arbitrary graph is -hard by reducing the problem of finding the maximum clique size of a graph to the g-centroid location problem. They have also given an efficient polynomial time algorithm for locating the g-centroid for maximal outerplanar graphs, Ptolemaic graphs, and split graphs. In this paper, we present an O(nm) time algorithm for locating the g-centroid for cographs, where n is the number of vertices and m is the number of edges of the graph.