تعداد نشریات | 5 |
تعداد شمارهها | 111 |
تعداد مقالات | 1,247 |
تعداد مشاهده مقاله | 1,199,763 |
تعداد دریافت فایل اصل مقاله | 1,060,528 |
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 | ||
[1] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Domination in graphs: advanced topics, Marcel Dekker, 1998.
[2] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of domination in graphs, CRC Press, 1998.
[3] M.A. Henning, Signed total domination in graphs, Discrete Math. 278 (2004), no. 1, 109–125.
[4] E. Shan and T.C.E. Cheng, Remarks on the minus (signed) total domination in graphs, Discrete Math. 308 (2008), no. 15, 3373–3380.
[5] S.M. Sheikholeslami and L. Volkmann, Signed total k-domination numbers of a directed graphs, An. St. Univ. Ovidius Constanta. 18 (2010), no. 2, 241–252.
[6] L. Volkmann, Signed total Roman k-domination in graphs, submitted.
[7] L. Volkmann, Signed total Roman domination in graphs, J. Comb. Optim. 32 (2016), no. 3, 855–871.
[8] L. Volkmann, Signed total Roman domination in digraphs, Discuss. Math. Graph Theory. 37 (2017), no. 1, 261–272.
[9] C. Wang, The signed k-domination numbers in graphs, Ars Combin. 106 (2012), 205–211.
[10] B. Zelinka, Signed total domination numbers of a graph, Czechoslovak Math. J. 51 (2001), no. 2, 225–229.
| ||
آمار تعداد مشاهده مقاله: 2,030 تعداد دریافت فایل اصل مقاله: 1,770 |