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On the signed Roman edge k-domination in graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 2، شماره 1، شهریور 2017، صفحه 57-64 اصل مقاله (406.89 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2017.25962.1061 | ||
| نویسنده | ||
| Akram Mahmoodi* | ||
| Department of Mathematics Payame Noor University I.R. Iran | ||
| چکیده | ||
| Let $k\geq 1$ be an integer, and $G=(V,E)$ be a finite and simple graph. The closed neighborhood $N_G[e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$. A signed Roman edge $k$-dominating function (SREkDF) on a graph $G$ is a function $f:E \rightarrow \{-1,1,2\}$ satisfying the conditions that (i) for every edge $e$ of $G$, $\sum _{x\in N[e]} f(x)\geq k$ and (ii) every edge $e$ for which $f(e)=-1$ is adjacent to at least one edge $e'$ for which $f(e')=2$. The minimum of the values $\sum_{e\in E}f(e)$, taken over all signed Roman edge $k$-dominating functions $f$ of $G$, is called the signed Roman edge $k$-domination number of $G$ and is denoted by $\gamma'_{sRk}(G)$. In this paper we establish some new bounds on the signed Roman edge $k$-domination number. | ||
| کلیدواژهها | ||
| signed Roman edge k-dominating function؛ signed Roman edge k-domination number؛ Domination number | ||
| مراجع | ||
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[1] H. Abdollahzadeh Ahangar, J. Amjadi, S.M. Sheikholeslami, L. Volkmann, and Y. Zhao, Signed Roman edge domination numbers in graphs, J. Comb. Optim. 31 (2016), no. 1, 333–346.
[2] H. Abdollahzadeh Ahangar, M.A. Henning, C. Löwenstein, Y. Zhao, and V. Samodivkin, Signed Roman domination in graphs, J. Comb. Optim. 27 (2014), no. 2, 241– 255.
[3] L. Asgharsharghi, S.M. Sheikholeslami, and L. Volkmann, Signed Roman edge k-domination in graphs, Discuss. Math. Graph Theory 37 (2017), no. 1, 39–53.
[4] M.A. Henning and L. Volkmann, Signed Roman k-domination in trees, Discrete Appl. Math. 186 (2015), 98–105.
[5] M.A. Henning and L. Volkmann, Signed Roman k-domination in graphs., Graphs & Combin. 32 (2016), no. 1, 175–190. | ||
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