On families of convex polytopes with constant metric dimension

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

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)

Abstract

Let G be a connected graph and d(x,y) be the distance between the vertices x and y. A subset of vertices W=w1,w2,...,wk is called a resolving set for G if for every two distinct vertices x,y∈V(G), there is a vertex wi∈W such that d(x,wi)≠d(y,wi). A resolving set containing a minimum number of vertices is called a metric basis for G and the number of vertices in a metric basis is its metric dimension dim(G). A family G of connected graphs is a family with constant metric dimension if dim(G) is finite and does not depend upon the choice of G in G. In this paper, we study the metric dimension of some classes of convex polytopes which are obtained by the combinations of two different graph of convex polytopes. It is shown that these classes of convex polytopes have the constant metric dimension and only three vertices chosen appropriately suffice to resolve all the vertices of these classes of convex polytopes.

Original languageEnglish
Pages (from-to)2629-2638
Number of pages10
JournalComputers and Mathematics with Applications
Volume60
Issue number9
DOIs
Publication statusPublished - Nov 2010
Externally publishedYes

Keywords

  • Antiprism
  • Basis
  • Convex polytope
  • Metric dimension
  • Prism
  • Resolving set

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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