Computing the metric dimension of convex polytopes generated by wheel related graphs

M. Imran, H. M.A. Siddiqui

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)

Abstract

An ordered set W= { w1,.. , wk} ⫅ V(G) of vertices of G is called a resolving set or locating set for G if every vertex is uniquely determined by its vector of distances to the vertices in W. A resolving set of minimum cardinality is called a metric basis for G and this cardinality is the metric dimension or location number of G, denoted by β(G). The metric dimension of certain wheel related graphs has been studied recently in [22]. In this paper, we extend this study to infinite classes of convex polytopes generated by wheel related graphs. We prove that these infinite classes of convex polytopes generated by wheel related graphs have unbounded metric dimension. It is natural to ask for the characterization of graphs with unbounded metric dimension.

Original languageEnglish
Pages (from-to)10-30
Number of pages21
JournalActa Mathematica Hungarica
Volume149
Issue number1
DOIs
Publication statusPublished - Jun 2016
Externally publishedYes

Keywords

  • basis
  • convex polytope
  • metric dimension
  • resolving set
  • wheel related graph

ASJC Scopus subject areas

  • Mathematics(all)

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