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An optimal locating-dominating set in the infinite triangular grid
Tekijät: Honkala I
Kustantaja: ELSEVIER SCIENCE BV
Julkaisuvuosi: 2006
Journal: Discrete Mathematics
Tietokannassa oleva lehden nimi: DISCRETE MATHEMATICS
Lehden akronyymi: DISCRETE MATH
Vuosikerta: 306
Numero: 21
Aloitussivu: 2670
Lopetussivu: 2681
Sivujen määrä: 12
ISSN: 0012-365X
DOI: https://doi.org/10.1016/j.disc.2006.04.028(external)
Tiivistelmä
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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