In 1998, Pandu Rangan et al. Proved that
locating the g-centroid for an arbitrary graph is
𝒩𝒫-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.