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Further results on maximal rainbow domination number | ||
| Transactions on Combinatorics | ||
| مقاله 29، دوره 9، شماره 4، اسفند 2020، صفحه 201-210 اصل مقاله (249.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2020.120014.1684 | ||
| نویسنده | ||
| Hossein Abdollahzadeh Ahangar* | ||
| Department of Mathematics, Babol Noshirvani University of Technology, Babol, I.R. Iran | ||
| چکیده | ||
| A 2-rainbow dominating function (2RDF) of a graph $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,2\}$ such that for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u\in N(v)}f(u)=\{1,2\}$ is fulfilled, where $N(v)$ is the open neighborhood of $v$. A maximal 2-rainbow dominating function of a graph $G$ is a $2$-rainbow dominating function $f$ such that the set $\{w\inV(G)|f(w)=\emptyset\}$ is not a dominating set of $G$. The weight of a maximal 2RDF $f$ is the value $\omega(f)=\sum_{v\in V}|f (v)|$. The maximal $2$-rainbow domination number of a graph $G$, denoted by $\gamma_{m2r}(G)$, is the minimum weight of a maximal 2RDF of $G$. In this paper, we continue the study of maximal 2-rainbow domination {number} in graphs. Specially, we first characterize all graphs with large maximal 2-rainbow domination number. Finally, we determine the maximal $2$-rainbow domination number in the sun and sunlet graphs. | ||
| کلیدواژه‌ها | ||
| $2$-rainbow dominating function؛ $2$-rainbow domination number؛ maximal $2$-rainbow dominating function؛ maximal $2$-rainbow domination number | ||
| مراجع | ||
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