%0 Journal Article
%T A note on the Roman domatic number of a digraph
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Volkmann, Lutz
%A Meierling, D.
%D 2020
%\ 06/01/2020
%V 5
%N 1
%P 19-26
%! A note on the Roman domatic number of a digraph
%K Digraphs
%K Roman dominating function
%K Roman domination number
%K Roman domatic number
%R 10.22049/cco.2019.26419.1107
%X Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling$fcolon V(D)to {0, 1, 2}$such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ ofRoman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,is called a {em Roman dominating family} (of functions) on $D$. The maximum number of functions in aRoman dominating family on $D$ is the {em Roman domatic number} of $D$, denoted by $d_{R}(D)$.In this note, we study the Roman domatic number in digraphs, and we present some sharpbounds for $d_{R}(D)$. In addition, we determine the Roman domatic number of some digraphs.Some of our results are extensions of well-known properties of the Roman domatic number ofundirected graphs.
%U http://comb-opt.azaruniv.ac.ir/article_13884_bf374c8fd79d776bfc11bd95660ff3b1.pdf