On the metric dimension of convex polytopes

Muhammad Imran, Syed Ahtsham Ul Haq Bokhary, A. Q. Baig

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 {pipe}V(G){pipe}=φ(n) and (Formula presented.) 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. 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 properties of of some classes of convex polytopes having pendent edges with respect to their metric dimension.

Original languageEnglish
Pages (from-to)295-307
Number of pages13
JournalAKCE International Journal of Graphs and Combinatorics
Volume10
Issue number3
Publication statusPublished - Oct 2013
Externally publishedYes

Keywords

  • Basis
  • Convex polytope
  • Metric dimension
  • Pendant
  • Plane graph
  • Resolving set

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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