TY - JOUR
AU - Sheikholeslami, Seyed Mahmoud
AU - Dehgardi, Nasrin
AU - Volkmann, Lutz
AU - Meierling, Dirk
PY - 2016/12/30
Y2 - 2022/05/24
TI - The Roman bondage number of a digraph
JF - Tamkang Journal of Mathematics
JA - Tamkang J. Math.
VL - 47
IS - 4
SE -
DO - 10.5556/j.tkjm.47.2016.2100
UR - https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2100
SP - 421-431
AB - Let $D=(V,A)$ be a finite and simple digraph. A Roman dominating function on $D$ is a labeling $f:V (D)\rightarrow \{0, 1, 2\}$ such that every vertex with label 0 has an in-neighbor with label 2. The weight of an RDF $f$ is the value $\omega(f)=\sum_{v\in V}f (v)$. The minimum weight of a Roman dominating function on a digraph $D$ is called the Roman domination number, denoted by $\gamma_{R}(D)$. The Roman bondage number $b_{R}(D)$ of a digraph $D$ with maximum out-degree at least two is the minimum cardinality of all sets $A'\subseteq A$ for which $\gamma_{R}(D-A')>\gamma_R(D)$. In this paper, we initiate the study of the Roman bondage number of a digraph. We determine the Roman bondage number in several classes of digraphs and give some sharp bounds.
ER -