On the metric dimension of circulant and Harary graphs

Journal article

Grigorious, Cyriac, Manuel, Paul, Miller, Mirka, Rajan, Bharati and Stephen, Sudeep. (2014). On the metric dimension of circulant and Harary graphs. Applied Mathematics and Computation. 248, pp. 47-54. https://doi.org/10.1016/j.amc.2014.09.045
AuthorsGrigorious, Cyriac, Manuel, Paul, Miller, Mirka, Rajan, Bharati and Stephen, Sudeep
Abstract

A metric generator is a set W of vertices of a graph G(V, E) such that for every pair of vertices u; v of G, there exists a vertex w ϵ W with the condition that the length of a shortest path from u to w is different from the length of a shortest path from v to w. In this case the vertex w is said to resolve or distinguish the vertices u and v. The minimum cardinality of a metric generator for G is called the metric dimension. The metric dimension problem is to find a minimum metric generator in a graph G. In this paper, we make a significant advance on the metric dimension problem for circulant graphs C (n, ±{1, 2, . . . , j}), 1 ⩽ j ⩽ ⎿n/2⏌, n ⩾ 3, and Harary graphs.

KeywordsMetric basis ; Metric dimension ; Circulant graphs ; Harary graphs
Year01 Jan 2014
JournalApplied Mathematics and Computation
Journal citation248, pp. 47-54
PublisherAcademic Press (Elsevier)
ISSN0096-3003
Digital Object Identifier (DOI)https://doi.org/10.1016/j.amc.2014.09.045
Web address (URL)https://www.sciencedirect.com/science/article/pii/S0096300314012703?via%3Dihub
Research or scholarlyResearch
Page range47-54
Publisher's version
File Access Level
Controlled
Output statusPublished
Publication dates
Online14 Oct 2014
PrintDec 2014
Publication process dates
Deposited21 May 2024
Additional information

© 2014 Elsevier Inc. All rights reserved.

Place of publicationUnited States
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