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
Authors | Grigorious, Cyriac, Manuel, Paul, Miller, Mirka, Rajan, Bharati and Stephen, Sudeep |
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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. |
Keywords | Metric basis ; Metric dimension ; Circulant graphs ; Harary graphs |
Year | 01 Jan 2014 |
Journal | Applied Mathematics and Computation |
Journal citation | 248, pp. 47-54 |
Publisher | Academic Press (Elsevier) |
ISSN | 0096-3003 |
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 scholarly | Research |
Page range | 47-54 |
Publisher's version | File Access Level Controlled |
Output status | Published |
Publication dates | |
Online | 14 Oct 2014 |
Dec 2014 | |
Publication process dates | |
Deposited | 21 May 2024 |
Additional information | © 2014 Elsevier Inc. All rights reserved. |
Place of publication | United States |
https://acuresearchbank.acu.edu.au/item/907q1/on-the-metric-dimension-of-circulant-and-harary-graphs
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