Geodesic
The Rainbow Domination Number of a Digraph
Kragujevac Journal of Mathematics, Tome 37 (2013) no. 2, p. 257 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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 
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     author = {J. Amjadi and A. Bahremandpour and S. M. Sheikholeslami and L. Volkmann},
     title = {The {Rainbow} {Domination} {Number} of a {Digraph}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {257 },
     year = {2013},
     volume = {37},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a4/}
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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/