On classes of regular graphs with constant metric dimension

Muhammad Imran, Syed Ahtsham ul Haq Bokhary, Ali Ahmad, Andrea Semaničová-feňovčíková

Research output: Contribution to journalArticlepeer-review

37 Citations (Scopus)

Abstract

In this paper, we are dealing with the study of the metric dimension of some classes of regular graphs by considering a class of bridgeless cubic graphs called the flower snarks Jn, a class of cubic convex polytopes considering the open problem raised in [M. Imran et al., families of plane graphs with constant metric dimension, Utilitas Math., in press] and finally Harary graphs H5,n by partially answering to an open problem proposed in [I. Javaid et al., Families of regular graphs with constant metric dimension, Utilitas Math., 2012, 88: 43-57]. We prove that these classes of regular graphs have constant metric dimension. It is natural to ask for the characterization of regular graphs with constant metric dimension.

Original languageEnglish
Pages (from-to)187-206
Number of pages20
JournalActa Mathematica Scientia
Volume33
Issue number1
DOIs
Publication statusPublished - Jan 2013
Externally publishedYes

Keywords

  • Basis
  • Convex polytope
  • Cubic graph
  • Flower snark
  • Metric dimension
  • Resolving set

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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