Optimal Locating-Total Dominating Sets in Strips of Height 3

• Autorzy: Ville Junnila
• Języki publikacji: EN

Abstrakty

EN

A set C of vertices in a graph G = (V,E) is total dominating in G if all vertices of V are adjacent to a vertex of C. Furthermore, if a total dominating set C in G has the additional property that for any distinct vertices u, v ∈ V \ C the subsets formed by the vertices of C respectively adjacent to u and v are different, then we say that C is a locating-total dominating set in G. Previously, locating-total dominating sets in strips have been studied by Henning and Jafari Rad (2012). In particular, they have determined the sizes of the smallest locating-total dominating sets in the finite strips of height 2 for all lengths. Moreover, they state as open question the analogous problem for the strips of height 3. In this paper, we answer the proposed question by determining the smallest sizes of locating-total dominating sets in the finite strips of height 3 as well as the smallest density in the infinite strip of height 3.

Słowa kluczowe

EN

locating-total dominating set; domination; square grid; strip.

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2015
• Tom: 35
• Numer: 3
• Strony: 447-462

Daty

wydano

2015-08-01

otrzymano

2013-12-04

poprawiono

2014-09-01

zaakceptowano

2014-09-01

online

2015-07-29

Twórcy

autor

Ville Junnila

• Department of Mathematics and Statistics University of Turku, FI-20014 Turku, Finland

Bibliografia

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• [7] T.W. Haynes, M.A. Henning and J. Howard, Locating and total dominating sets in trees, Discrete Appl. Math. 154 (2006) 1293-1300. doi:10.1016/j.dam.2006.01.002[Crossref]
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Identyfikatory

DOI

10.7151/dmgt.1805