R-sets and metric dimension of necklace graphs

Ioan Tomescu, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

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
Volume9
Issue number1
DOIs
Publication statusPublished - 2015
Externally publishedYes

Keywords

  • Diameter
  • Exchange property
  • Metric dimension
  • Necklace graph
  • R-set

ASJC Scopus subject areas

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

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