On the metric dimension of circulant and Harary graphs

Title: On the metric dimension of circulant and Harary graphs
Creator: Grigorious, Cyriac; Manuel, Paul; Miller, Mirka; Rajan, Bharati; Stephen, Sudeep
Relation: Applied Mathematics and Computation Vol. 248, p. 47-54
Publisher Link: http://dx.doi.org/10.1016/j.amc.2014.09.045
Publisher: Elsevier
Resource Type: journal article
Date: 2014
Description: 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∈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 for Harary graphs.
Subject: metric basis; metric dimension; circulant graphs; Harary graphs
Identifier: http://hdl.handle.net/1959.13/1297367
Identifier: uon:19436
Identifier: ISSN:0096-3003
Language: eng
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