@article {
author = {Xie, Zhihong and Hao, Guoliang and Wei, Shouliu},
title = {The Roman domination and domatic numbers of a digraph},
journal = {Communications in Combinatorics and Optimization},
volume = {4},
number = {1},
pages = {47-59},
year = {2019},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2019.26356.1101},
abstract = {A Roman dominating function (RDF) on a digraph $D$ is a function $f: V(D)\rightarrow {0,1,2}$ satisfying the condition that every vertex $v$ with $f(v)=0$ has an in-neighbor $u$ with $f(u)=2$. The weight of an RDF $f$ is the value $\sum_{v\in V(D)}f(v)$. The Roman domination number of a digraph $D$ is the minimum weight of an RDF on $D$. A set $\{f_1,f_2,\dots,f_d\}$ of Roman dominating functions on $D$ with the property that $\sum_{i=1}^df_i(v)\le2$ 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 paper we continue the investigation of the Roman domination number, and we initiate the study of the Roman domatic number in digraphs. We present some bounds for $d_{R}(D)$. In addition, we determine the Roman domatic number of some digraphs.},
keywords = {Roman dominating function,Roman domination number,Roman domatic number,digraph},
url = {http://comb-opt.azaruniv.ac.ir/article_13841.html},
eprint = {http://comb-opt.azaruniv.ac.ir/article_13841_9bb2c1e1cb7db1916a327f1866d037b2.pdf}
}