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Restrained roman domination in graphs | ||
| Transactions on Combinatorics | ||
| مقاله 1، دوره 4، شماره 1، خرداد 2015، صفحه 1-17 اصل مقاله (273.85 K) | ||
| نوع مقاله: National Conference on Labelings and Decompositions of Graphs | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2015.4395 | ||
| نویسندگان | ||
| Roushini Leely Pushpam* 1؛ Sampath Padmapriea2 | ||
| 1Department of Mathematics D.B.Jain College, Chennai 97 India | ||
| 2Department of Mathematics Sri Sairam Engineering College Chennai 44 India | ||
| چکیده | ||
| A \textit{Roman dominating function} (RDF) on a graph $G = (V,E)$ is defined to be a function $ f:V \rightarrow \lbrace 0,1,2\rbrace$ 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 set $S \subseteq V$ is a \textit{Restrained dominating set} if every vertex not in $S$ is adjacent to a vertex in $S$ and to a vertex in $V - S$. We define a \textit{Restrained Roman dominating function} on a graph $G = (V,E)$ to be a function $f : V \rightarrow \lbrace 0,1,2 \rbrace$ satisfying the condition that every vertex $u$ for which $f(u) = 0 $ is adjacent to at least one vertex $v$ for which $f(v)=2$ and at least one vertex $w$ for which $f(w) = 0$. The \textit{weight} of a Restrained Roman dominating function is the value $f(V)= \sum _{u \in V} f(u)$. The minimum weight of a Restrained Roman dominating function on a graph $G$ is called the Restrained Roman domination number of $G$ and denoted by $\gamma_{rR}(G)$. In this paper, we initiate a study of this parameter. | ||
| کلیدواژهها | ||
| domination؛ Roman domination؛ Restrained domination | ||
| مراجع | ||
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