The metric dimension of two-dimensional extended meshes

Adar, Ron and Epstein, Leah: The metric dimension of two-dimensional extended meshes. Acta cybernetica, (23) 3. pp. 761-772. (2018)

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Abstract

We consider two-dimensional grids with diagonals, also called extended meshes or meshes. Such a graph consists of vertices of the form (i, j) for 1 ≤ i ≤ m and 1 ≤ j ≤ n, for given m, n ≥ 2. Two vertices are defined to be adjacent if the `∞ distance between their vectors is equal to 1. A landmark set is a subset of vertices L ⊆ V , such that for any distinct pair of vertices u, v ∈ V , there exists a vertex of L with different distances to u and v. We analyze the metric dimension and show how to obtain a landmark set of minimum cardinality.

Item Type: Article
Journal or Publication Title: Acta cybernetica
Date: 2018
Volume: 23
Number: 3
Page Range: pp. 761-772
ISSN: 0324-721X
Uncontrolled Keywords: Matematika, Metrikus dimenzió
Additional Information: Bibliogr.: p. 771-772. ; Összefoglalás angol nyelven
Date Deposited: 2018. Nov. 07. 14:47
Last Modified: 2018. Nov. 07. 14:47
URI: http://acta.bibl.u-szeged.hu/id/eprint/55675

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