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On Metric Dimensions of Symmetric Graphs Obtained by Rooted Product

Authors
  • imran, shahid
  • siddiqui, muhammad kamran
  • imran, muhammad
  • hussain, muhammad
Publication Date
Oct 08, 2018
Identifiers
DOI: 10.3390/math6100191
OAI: oai:mdpi.com:/2227-7390/6/10/191/
Source
MDPI
Keywords
Language
English
License
Green
External links

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.

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