METRIC DIMENSION AND DIAMETER IN BIPARTITE GRAPHS

Peter Dankelmann, Jane Morgan, Emily Rivett-Carnac

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Let G be a connected graph and W a set of vertices of G. If every vertex of G is determined by its distances to the vertices in W, then W is said to be a resolving set. The cardinality of a minimum resolving set is called the metric dimension of G. In this paper we determine the maximum number of vertices in a bipartite graph of given metric dimension and diameter. We also determine the minimum metric dimension of a bipartite graph of given maximum degree.

Original languageEnglish
Pages (from-to)487-498
Number of pages12
JournalDiscussiones Mathematicae - Graph Theory
Volume43
Issue number2
DOIs
Publication statusPublished - 2023

Keywords

  • bipartite graph
  • diameter
  • maximum degree
  • metric dimension
  • resolving set

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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