TY - JOUR
ID - 13884
TI - A note on the Roman domatic number of a digraph
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Volkmann, Lutz
AU - Meierling, D.
AD - RWTH Aachen University
Y1 - 2020
PY - 2020
VL - 5
IS - 1
SP - 19
EP - 26
KW - Digraphs
KW - Roman dominating function
KW - Roman domination number
KW - Roman domatic number
DO - 10.22049/cco.2019.26419.1107
N2 - A 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 Roman dominating family (of functions) on $D$. The maximum number of functions in a Roman dominating family on $D$ is the 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.
UR - http://comb-opt.azaruniv.ac.ir/article_13884.html
L1 - http://comb-opt.azaruniv.ac.ir/article_13884_bf374c8fd79d776bfc11bd95660ff3b1.pdf
ER -