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 
@article{KJM_2013_37_2_a4,
     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 },
     publisher = {mathdoc},
     volume = {37},
     number = {2},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a4/}
}
TY  - JOUR
AU  - J. Amjadi
AU  - A. Bahremandpour
AU  - S. M. Sheikholeslami
AU  - L. Volkmann
TI  - The Rainbow Domination Number of a Digraph
JO  - Kragujevac Journal of Mathematics
PY  - 2013
SP  - 257 
VL  - 37
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a4/
LA  - en
ID  - KJM_2013_37_2_a4
ER  - 
%0 Journal Article
%A J. Amjadi
%A A. Bahremandpour
%A S. M. Sheikholeslami
%A L. Volkmann
%T The Rainbow Domination Number of a Digraph
%J Kragujevac Journal of Mathematics
%D 2013
%P 257 
%V 37
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KJM_2013_37_2_a4/
%G en
%F KJM_2013_37_2_a4
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/