On resolvability and exchange property in antiweb-wheels

Rishi Naeem, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Metric dimension 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)| = ℓ(n) and lim ℓ(n) = ∞. If there exists a constant C > 0 such that β(Gn) ≤ C for every n ≥ 1 then we shall say that F has bounded metric dimension, otherwise T 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 antiweb-wheels. We determine the exact value of metric dimension for antiweb-wheels and prove that they have unbounded 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 antiweb-wheels.

Original languageEnglish
Pages (from-to)187-200
Number of pages14
JournalUtilitas Mathematica
Volume104
Publication statusPublished - Sep 2017
Externally publishedYes

Keywords

  • Antiweb-wheel
  • Basis
  • Exchange property
  • Metric dimension
  • Resolving set

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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