The median function on graphs with bounded profiles

Authors:
Kannan Balakrishnan;Manoj Changat;Sandi Klavar
Affiliations:
Department of Computer Applications, Cochin University of Science and Technology, Cochin-22, India;Department of Futures Studies, University of Kerala, Trivandrum, India;Department of Mathematics and Computer Science, FNM, University of Maribor, Gosposvetska 84, 2000 Maribor, Slovenia
Venue:
Discrete Applied Mathematics
Year:
2008

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Abstract

The median of a profile @p=(u"1,...,u"k) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of @p. It is shown that for profiles @p with diameter @q the median set can be computed within an isometric subgraph of G that contains a vertex x of @p and the r-ball around x, where r2@q-1-2@q/|@p|. The median index of a graph and r-joins of graphs are introduced and it is shown that r-joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.