An efficient g‐centroid location algorithm for cographs

Abstract

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

Symbolic Regression for Approximating Graph Geodetic Number

“…Related notions are the graph hull number [14] and the domination number [15]. All these concepts have practical applications, e.g., in public transportation design [9], in achievement and avoidance games [8], in location problems [25], in maximizing the switchboard numbers on telephone tree graphs [23], in mobile ad hoc networks [26], and in design of efficient typologies for parallel computing [24].…”