On metric dimensions of symmetric graphs obtained by rooted product

Shahid Imran, Muhammad Kamran Siddiqui, Muhammad Imran, Muhammad Hussain

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Let G = (V, E) be a connected graph and d(x, y) be the distance between the vertices x and y 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). In this paper, Cycle, Path, Harary graphs and their rooted product as well as their connectivity are studied and their metric dimension is calculated. It is proven that metric dimension of some graphs is unbounded while the other graphs are constant, having three or four dimensions in certain cases.

Original languageEnglish
Article number191
JournalMathematics
Volume6
Issue number10
DOIs
Publication statusPublished - Oct 8 2018

Keywords

  • Basis
  • Cycle
  • Harary graphs
  • Metric dimension
  • Path
  • Resolving set
  • Rooted product

ASJC Scopus subject areas

  • Mathematics(all)

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