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Bounds on the restrained Roman domination number of a graph | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 1، شماره 1، شهریور 2016، صفحه 75-82 اصل مقاله (392.3 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2016.13556 | ||
| نویسندگان | ||
| H. Abdollahzadeh Ahangar* 1؛ S.R. Mirmehdipour2 | ||
| 1Babol Noshirvani University of Technology | ||
| 2Babol Noshirvani University of Technology | ||
| چکیده | ||
| A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) =2$. A {\em restrained Roman dominating} function $f$ is a Roman dominating function if the vertices with label 0 induce a subgraph with no isolated vertex. The weight of a restrained Roman dominating function is the value $\omega(f)=\sum_{u\in V(G)} f(u)$. The minimum weight of a restrained Roman dominating function of $G$ is called the { \em restrained Roman domination number} of $G$ and denoted by $\gamma_{rR}(G)$. In this paper we establish some sharp bounds for this parameter. | ||
| کلیدواژه‌ها | ||
| Roman dominating function؛ Roman domination number؛ restrained Roman dominating function؛ restrained Roman domination number | ||
| مراجع | ||
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