A1 Refereed original research article in a scientific journal
An optimal locating-dominating set in the infinite triangular grid
Authors: Honkala I
Publisher: ELSEVIER SCIENCE BV
Publication year: 2006
Journal: Discrete Mathematics
Journal name in source: DISCRETE MATHEMATICS
Journal acronym: DISCRETE MATH
Volume: 306
Issue: 21
First page : 2670
Last page: 2681
Number of pages: 12
ISSN: 0012-365X
DOI: https://doi.org/10.1016/j.disc.2006.04.028(external)
Abstract
Assume that G = (V, E) is an undirected graph, and C subset of V. For every v is an element of V, we denote by I (v) the set of all elements of C that are within distance one from v. If all the sets I (v) for v is an element of V\C are non-empty, and pairwise different, then C is called a locating-dominating set. The smallest possible density of a locating-dominating set in the infinite triangular grid is shown to be (13)/(57) (c) 2006 Elsevier B.V. All rights reserved.
Assume that G = (V, E) is an undirected graph, and C subset of V. For every v is an element of V, we denote by I (v) the set of all elements of C that are within distance one from v. If all the sets I (v) for v is an element of V\C are non-empty, and pairwise different, then C is called a locating-dominating set. The smallest possible density of a locating-dominating set in the infinite triangular grid is shown to be (13)/(57) (c) 2006 Elsevier B.V. All rights reserved.
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