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Computing the Metric Dimension of Gear Graphs

Authors
  • imran, shahid
  • siddiqui, muhammad kamran
  • imran, muhammad
  • hussain, muhammad
  • bilal, hafiz muhammad
  • cheema, imran zulfiqar
  • tabraiz, ali
  • saleem, zeeshan
Publication Date
Jun 08, 2018
Identifiers
DOI: 10.3390/sym10060209
OAI: oai:mdpi.com:/2073-8994/10/6/209/
Source
MDPI
Keywords
Language
English
License
Green
External links

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 &cong / 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.

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