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2-rainbow domination number of the subdivision of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 6، دوره 11، شماره 1، خرداد 2026، صفحه 79-91 اصل مقاله (429.8 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.28850.1749 | ||
| نویسندگان | ||
| Rostam Yarke Salkhori؛ Ebrahim Vatandoost؛ Ali Behtoei* | ||
| Department of Mathematics, Faculty of Science, Imam Khomeini International University | ||
| چکیده | ||
| Let $G$ be a simple graph and $f : V (G) \rightarrow P(\{1,2\})$ be a function where for each vertex $v \in V (G)$ with $f(v)= \emptyset$ we have $\bigcup_{u \in N_{G}(v)} f(u) = \{1,2\}.$ Then $f$ is a $2$-rainbow dominating function (a $2RDF$) of $G.$ The weight of $f$ is $\omega(f)=\sum_{v \in V(G)} |f(v)|.$ The minimum weight among all of $2-$rainbow dominating functions is $2-$rainbow domination number and is denoted by $\gamma_{r2}(G)$. In this paper, we provide some bounds for the $2-$rainbow domination number of the subdivision graph $S(G)$ of a graph $G$. Also, among some other interesting results, we determine the exact value of $\gamma_{r2}(S(G))$ when $G$ is a tree, a bipartite graph, $K_{r,s}$, $K_{n_1,n_2,\dots,n_k}$ and $K_n$. | ||
| کلیدواژهها | ||
| $2$-rainbow domination number؛ subdivision؛ bipartite graph؛ tree | ||
| مراجع | ||
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