On the Metric Dimension of Generalized Petersen Multigraphs

Muhammad Imran, Muhammad Kamran Siddiqui, Rishi Naeem

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

In this paper, we study the metric dimension of barycentric subdivision of Möbius ladders and the metric dimension of generalized Petersen multigraphs. We prove that the generalized Petersen multigraphs denoted by P(2n,n) have metric dimension 3 when n is even and 4 otherwise. We also study the exchange property for resolving sets of barycentric subdivisions of Möbius ladders and generalized Petersen multigraphs and prove that the exchange property of the bases in a vector space does not hold for minimal resolving sets of these graphs.

Original languageEnglish
Article number8554062
Pages (from-to)74328-74338
Number of pages11
JournalIEEE Access
Volume6
DOIs
Publication statusPublished - 2018

Keywords

  • Metric dimension
  • Möbius ladders
  • barycentric subdivision
  • basis
  • generalized Petersen graphs
  • resolving set

ASJC Scopus subject areas

  • Computer Science(all)
  • Materials Science(all)
  • Engineering(all)

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