Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-21285120200601A note on the Roman domatic number of a digraph19261388410.22049/cco.2019.26419.1107ENLutzVolkmannRWTH Aachen University0000-0003-3496-277XD.MeierlingRWTH Aachen UniversityJournal Article20190201Roman dominating function} on a digraph $D$ with vertex set $V(D)$ is a labeling<br />$fcolon V(D)to {0, 1, 2}$<br />such that every vertex with label $0$ has an in-neighbor with label $2$. A set ${f_1,f_2,ldots,f_d}$ of<br />Roman dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$,<br />is called a {em Roman dominating family} (of functions) on $D$. The maximum number of functions in a<br />Roman dominating family on $D$ is the {em Roman domatic number} of $D$, denoted by $d_{R}(D)$.<br />In this note, we study the Roman domatic number in digraphs, and we present some sharp<br />bounds for $d_{R}(D)$. In addition, we determine the Roman domatic number of some digraphs.<br />Some of our results are extensions of well-known properties of the Roman domatic number of<br />undirected graphs.http://comb-opt.azaruniv.ac.ir/article_13884_bf374c8fd79d776bfc11bd95660ff3b1.pdf