Volkmann, L., Meierling, D. (2019). A note on the Roman domatic number of a digraph. Communications in Combinatorics and Optimization, (), -. doi: 10.22049/cco.2019.26419.1107

Lutz Volkmann; D. Meierling. "A note on the Roman domatic number of a digraph". Communications in Combinatorics and Optimization, , , 2019, -. doi: 10.22049/cco.2019.26419.1107

Volkmann, L., Meierling, D. (2019). 'A note on the Roman domatic number of a digraph', Communications in Combinatorics and Optimization, (), pp. -. doi: 10.22049/cco.2019.26419.1107

Volkmann, L., Meierling, D. A note on the Roman domatic number of a digraph. Communications in Combinatorics and Optimization, 2019; (): -. doi: 10.22049/cco.2019.26419.1107

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 ${f_1,f_2,ldots,f_d}$ of Roman 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 a Roman 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 sharp bounds 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 of undirected graphs.