@article{Sheikholeslami_Bodaghli_Volkmann_2016, title={Twin signed Roman domination numbers in directed graphs}, volume={47}, url={https://journals.math.tku.edu.tw/index.php/TKJM/article/view/2035}, DOI={10.5556/j.tkjm.47.2016.2035}, abstractNote={Let $D$ be a finite simple digraph with vertex set $V(D)$ and arc set $A(D)$. A twin signed Roman dominating function (TSRDF) on the digraph $D$ is a function $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the conditions that (i) $\sum_{x\in N^-[v]}f(x)\ge 1$ and $\sum_{x\in N^+[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ (resp. $N^+[v]$) consists of $v$ and all in-neighbors (resp. out-neighbors) of $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an in-neighbor $v$ and an out-neighbor $w$ for which $f(v)=f(w)=2$. The weight of an TSRDF $f$ is $\omega(f)=\sum_{v\in V(D)}f(v)$. The twin signed Roman domination number $\gamma_{sR}^*(D)$ of $D$ is the minimum weight of an TSRDF on $D$. In this paper, we initiate the study of twin signed Roman domination in digraphs and we present some sharp bounds on $\gamma_{sR}^*(D)$. In addition, we determine the twin signed Roman domination number of some classes of digraphs.}, number={3}, journal={Tamkang Journal of Mathematics}, author={Sheikholeslami, Seyed Mahmoud and Bodaghli, Asghar and Volkmann, Lutz}, year={2016}, month={Sep.}, pages={357-371} }