Metric dimension and exchange property for resolving sets in rotationally-symmetric graphs

Rishi Naeem, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


Metric dimension or location number is a generalization of affine dimension to arbitrary metric spaces (provided a resolving set exists). Let F be a family of connected graphs Gn: F = (Gn)n≥1 depending on n as follows: the order |V(G)| = φ(n) and. If there exists a constant C > 0 such that dim(Gn) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension, otherwise F has unbounded metric dimension. If all graphs in F have the same metric dimension (which does not depend on n), F is called a family with constant metric dimension. In this paper, we study the metric dimension of quasi flower snarks, generalized antiprism and cartesian product of square cycle and path. We prove that these classes of graphs have constant or bounded metric dimension. It is natural to ask for characterization of graphs classes with respect to the nature of their metric dimension. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of quasi flower snarks, generalized prism and generalized antiprism.

Original languageEnglish
Pages (from-to)1665-1674
Number of pages10
JournalApplied Mathematics and Information Sciences
Issue number4
Publication statusPublished - Jul 2014
Externally publishedYes


  • Basis
  • Exchange property
  • Metric dimension
  • Quasi flower snark
  • Resolving set

ASJC Scopus subject areas

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


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