On locating–dominating sets in infinite grids

Honkala, Iiro; Laihonen, Tero

doi:10.1016/j.ejc.2004.09.002

Cited by 31 publications

(30 citation statements)

References 7 publications

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“…The concept of locating-dominating codes was first introduced by Slater in [13,15,16] and later generalized by Carson in [3]. Locating-dominating codes have been since studied in various papers such as [2,6,7,9,10,14,[17][18][19]. For other papers on the subject, we refer to the Web site [12].…”

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Locating–dominating codes in paths

Exoo

Junnila

Laihonen

2011

Discrete Mathematics

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a b s t r a c tBertrand, Charon, Hudry and Lobstein studied, in their paper in 2004 [1], r-locatingdominating codes in paths P n . They conjectured that if r ≥ 2 is a fixed integer, then the smallest cardinality of an r-locating-dominating code in P n , denoted by M LD r (P n ), satisfies M LD r (P n ) = ⌈(n + 1)/3⌉ for infinitely many values of n. We prove that this conjecture holds. In fact, we show a stronger result saying that for any r ≥ 3 we have M LD r (P n ) = ⌈(n + 1)/3⌉ for all n ≥ n r when n r is large enough. In addition, we solve a conjecture on location-domination with segments of even length in the infinite path.

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“…For other papers on the subject, we refer to the Web site [12]. Moreover, location-domination in paths has been examined in [1,8] (for cycles see [5]). …”

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Locating–dominating codes in paths

Exoo

Junnila

Laihonen

2011

Discrete Mathematics

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“…Identifying codes in many different kinds of underlying graphs have been examined (see [6]). Among them are cycles and paths [1,3,8,11]; see also [2,4,9].…”

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Optimal Identifying Codes in Cycles and Paths

Junnila

Laihonen

2011

Graphs and Combinatorics

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“…The authors of the papers [23,24,27] study the single-fault-tolerant locating-dominating sets and an open neighborhood locating-dominating sets in trees. More information on locating-dominating sets can be found in [12,13,15,25].…”

Section: Introductionmentioning

confidence: 99%

“…For more information about these issues, see [3,9,14,15,21]. The authors of the papers [23,24,27] study the single-fault-tolerant locating-dominating sets and an open neighborhood locating-dominating sets in trees.…”

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confidence: 99%