An efficient <mml:math alttext="$g$" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>g</mml:mi></mml:math>-centroid location algorithm for cographs

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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

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.