R-Sets and Metric Dimension of Necklace Graphs

Ioan Tomescu, Muhammad Imran

Research output: Contribution to journalArticlepeer-review


The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. In this paper R-sets are used to show that metric dimension dim(Nen) = 3 when n is odd and 2 otherwise, where Nen is the necklace graph of order 2n + 2. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of Nen if n is even.

Original languageEnglish
Pages (from-to)63-67
Number of pages5
JournalApplied Mathematics and Information Sciences
Issue number1
Publication statusPublished - Jan 2015
Externally publishedYes


  • Metric dimension
  • R-set
  • diameter
  • exchange property
  • necklace graph

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics


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