Average distance in colored graphs

Peter Dankelmann, Wayne Goddard, Peter Slater

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


For a graph G where the vertices are colored, the colored distance of G is defined as the sum of the distances between all unordered pairs of vertices having different colors. Then for a fixed supply s of colors, ds(G) is defined as the minimum colored distance over all colorings with s. This generalizes the concepts of median and average distance. In this paper we explore bounds on this parameter, especially a natural lower bound and the particular case of balanced 2-colorings (equal numbers of red and blue). We show that the general problem is NP-hard but there is a polynomial-time algorithm for trees.

Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalJournal of Graph Theory
Issue number1
Publication statusPublished - Sept 2001
Externally publishedYes


  • Average distance
  • Colored graphs
  • Distance

ASJC Scopus subject areas

  • Geometry and Topology


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