Geodesic
The Rainbow Domination Number of a Digraph
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 257

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

Let $D=(V,A)$ be a finite and simple digraph. A II-rainbow dominating function} (2RDF) of a digraph $D$ is a function $f$ from the vertex set $V$ to the set of all subsets of the set $\{1,2\}$ such that for any vertex $v\in V$ with $f(v)=\emptyset$ the condition $\bigcup_{u\in N^-(v)}f(u)=\{1,2\}$ is fulfilled, where $N^-(v)$ is the set of in-neighbors of $v$. The weight of a 2RDF $f$ is the value $\omega(f)=\sum_{v\in V}|f (v)|$. The $2$-rainbow domination number of a digraph $D$, denoted by $\gamma_{r2}(D)$, is the minimum weight of a 2RDF of $D$. In this paper we initiate the study of rainbow domination in digraphs and we present some sharp bounds for $\gamma_{r2}(D)$.
Classification : 05C69 05C20
Keywords: Rainbow dominating function, Rainbow domination number, Digraph 
J. Amjadi; A. Bahremandpour; S. M. Sheikholeslami; L. Volkmann. The Rainbow Domination Number of a Digraph. Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 257 . http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a4/
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     title = {The {Rainbow} {Domination} {Number} of a {Digraph}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {257 },
     year = {2013},
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     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a4/}
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