@article{Sheikholeslami_Dehgardi_Volkmann_Meierling_2016, title={The Roman bondage number of a digraph}, volume={47}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2100}, DOI={10.5556/j.tkjm.47.2016.2100}, abstractNote={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.}, number={4}, journal={Tamkang Journal of Mathematics}, author={Sheikholeslami, Seyed Mahmoud and Dehgardi, Nasrin and Volkmann, Lutz and Meierling, Dirk}, year={2016}, month={Dec.}, pages={421-431} }