Computing the metric dimension of gear graphs

Shahid Imran, Muhammad Kamran Siddiqui, Muhammad Imran, Muhammad Hussain, Hafiz Muhammad Bilal, Imran Zulfiqar Cheema, Ali Tabraiz, Zeeshan Saleem

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

Let G = (V, E) be a connected graph and d(u, v) denote the distance between the vertices u and v in G. A set of vertices W resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G and is denoted by dim(G). Let J2n,m be a m-level gear graph obtained by m-level wheel graph W2n,m ≅ mC2n + k1 by alternatively deleting n spokes of each copy of C2n and J3n be a generalized gear graph obtained by alternately deleting 2n spokes of the wheel graph W3n. In this paper, the metric dimension of certain gear graphs J2n,m and J3n generated by wheel has been computed. Also this study extends the previous result given by Tomescu et al. in 2007.

Original languageEnglish
Article number209
JournalSymmetry
Volume10
Issue number6
DOIs
Publication statusPublished - Jun 1 2018

Keywords

  • Basis
  • Gear graph
  • Generalized gear graph
  • Metric dimension
  • Resolving set

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

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