@article{Amjadi_Khoeilar_Dehgardi_Volkmann_Sheikholeslami_2018, title={The restrained rainbow bondage number of a graph}, volume={49}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2365}, DOI={10.5556/j.tkjm.49.2018.2365}, abstractNote={A restrained $k$-rainbow dominating function (R$k$RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2,\ldots,k\}$ such that for any vertex $v \in V (G)$ with $f(v) = \emptyset$ the conditions $\bigcup_{u \in N(v)} f(u)=\{1,2,\ldots,k\}$ and $|N(v)\cap \{u\in V\mid f(u)=\emptyset\}|\ge 1$ are fulfilled, where $N(v)$ is the open neighborhood of $v$. The weight of a restrained $k$-rainbow dominating function is the value $w(f)=\sum_{v\in V}|f (v)|$. The minimum weight of a restrained $k$-rainbow dominating function of $G$ is called the restrained $k$-rainbow domination number of $G$, denoted by $\gamma_{rrk}(G)$. The restrained $k$-rainbow bondage number $b_{rrk}(G)$ of a graph $G$ with maximum degree at least two is the minimum cardinality of all sets $F \subseteq E(G)$ for which $\gamma_{rrk}(G-F) > \gamma_{rrk}(G)$. In this paper, we initiate the study of the restrained $k$-rainbow bondage number in graphs and we present some sharp bounds for $b_{rr2}(G)$. In addition, we determine the restrained 2-rainbow bondage number of some classes of graphs.}, number={2}, journal={Tamkang Journal of Mathematics}, author={Amjadi, Jafar and Khoeilar, Rana and Dehgardi, N. and Volkmann, Lutz and Sheikholeslami, S.M.}, year={2018}, month={Jun.}, pages={115-127} }