The Double Multicompetition Number of a Multigraph

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8845)

Abstract

The double competition multigraph of a digraph \(D\) is the multigraph which has the same vertex set as \(D\) and has \(m_{xy}\) multiple edges between two distinct vertices \(x\) and \(y\), where \(m_{xy}\) is defined to be the number of common out-neighbors of \(x\) and \(y\) in \(D\) times the number of common in-neighbors of \(x\) and \(y\) in \(D\).

In this paper, we introduce the notion of the double multicompetition number of a multigraph. It is easy to observe that, for any multigraph \(M\), \(M\) together with sufficiently many isolated vertices is the double competition multigraph of some acyclic digraph. The double multicompetition number of a multigraph is defined to be the minimum number of such isolated vertices. We give a characterization of multigraphs with bounded double multicompetition number and give a lower bound for the double multicompetition numbers of multigraphs.

Keywords

Intersection graph Double competition multigraph  Double multicompetition number Acyclic digraph 

2010 Mathematics Subject Classification

05C20 05C75 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsPusan National UniversityBusanKorea
  2. 2.Division of Information Engineering, Faculty of Engineering, Information and SystemsUniversity of TsukubaIbarakiJapan

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