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Signed total Roman k-domination in directed graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 1، شماره 2، اسفند 2016، صفحه 165-178 اصل مقاله (442.54 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2016.13576 | ||
| نویسندگان | ||
| Nasrin Dehgardi* 1؛ Lutz Volkmann2 | ||
| 1Sirjan University of Technology, Sirjan 78137, Iran | ||
| 2Lehrstuhl II fur Mathematik, RWTH Aachen University, 52056 Aachen, Germany | ||
| چکیده | ||
| Let $D$ be a finite and simple digraph with vertex set $V(D)$. A signed total Roman $k$-dominating function (STR$k$DF) on $D$ is a function $f:V(D)\rightarrow\{-1, 1, 2\}$ satisfying the conditions that (i) $\sum_{x\in N^{-}(v)}f(x)\ge k$ for each $v\in V(D)$, where $N^{-}(v)$ consists of all vertices of $D$ from which arcs go into $v$, and (ii) every vertex $u$ for which $f(u)=-1$ has an inner neighbor $v$ for which $f(v)=2$. The weight of an STR$k$DF $f$ is $\omega(f)=\sum_{v\in V (D)}f(v)$. The signed total Roman $k$-domination number $\gamma^{k}_{stR}(D)$ of $D$ is the minimum weight of an STR$k$DF on $D$. In this paper we initiate the study of the signed total Roman $k$-domination number of digraphs, and we present different bounds on $\gamma^{k}_{stR}(D)$. In addition, we determine the signed total Roman $k$-domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman $k$-domination number $\gamma^{k}_{stR}(G)$ of graphs $G$. | ||
| کلیدواژه‌ها | ||
| Digraph؛ Signed total Roman k-dominating function؛ Signed total Roman k-domination | ||
| مراجع | ||
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