International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 9, Pages 1405-1413
doi:10.1155/IJMMS.2005.1405

An efficient g-centroid location algorithm for cographs

V. Prakash

Department of Computer Science and Computer Engineering, La Trobe University Bundoora, Melbourne 3086, VIC, Australia

Received 19 August 2004; Revised 17 January 2005

Copyright © 2005 V. Prakash. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.