Extremal Digraphs for an Upper Bound on the Double Roman Domination Number

Ouldrabah, Lyes; Blidia, Mostafa; Bouchou, Ahmed; Volkmann, Lutz

doi:10.1007/s40840-019-00735-7

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2023

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“…In [6], we gave necessary conditions for digraphs D such that dR (D) = 2 (n + ) + 1 where + 1. Since we are interested in oriented trees, we state their results only for the class of oriented trees.…”

Section: Preliminary Resultsmentioning

confidence: 99%

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On the double Roman domination number in oriented trees

Ouldrabah

Bouchou

Blidia

2023

Preprint

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Note: Please see pdf for full abstract with equations. Let D = (V,A) be a digraph. A double Roman dominating function on a digraph D is a function ƒ :V → {0, 1, 2, 3} such that every vertex u for which ƒ(u) = 0 has an in-neighbor v for which ƒ(v) = 3 or at least two in-neighbors assigned 2 under ƒ, while if ƒ(u) = 1, then the vertex u must have at least one in-neighbor assigned 2 or 3. The weight of a double Roman dominating function is the value ƒ(V) = ∑v∈V ƒ(v). The minimum weight of a double Roman dominating function on a digraph D is called the double Roman domination number of D, denoted by γdR (D). This paper gives a descriptive characterization of oriented trees T satisfying γdR(T ) = 2 (n − Δ+) + 1. 2020 Mathematics Subject Classification: 05C20,05C69.

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Section: Preliminary Resultsmentioning

confidence: 99%

“…For digraphs, the de…nition of double Roman dominating function was introduced by Hao et al [3], and some results were given. In [6], we gave extremal k-out-regular digraphs with 1 k n 1 and tournaments, atteining the next upper bound, given in [3].…”

Section: Introductionmentioning

confidence: 99%