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On the Roman domination number of the subdivision of some graphs | ||
| Journal of Discrete Mathematics and Its Applications | ||
| دوره 9، شماره 4، اسفند 2024، صفحه 321-333 اصل مقاله (295.77 K) | ||
| نوع مقاله: Full Length Article | ||
| شناسه دیجیتال (DOI): 10.22061/jdma.2024.11309.1099 | ||
| نویسندگان | ||
| Rostam Yarke Salkhori* ؛ Ebrahim Vatandoost؛ Ali Behtoei | ||
| Imam Khomeini International University, P.O. Box 34148- 96818, Qazvin, I. R. Iran | ||
| تاریخ دریافت: 05 آبان 1403، تاریخ بازنگری: 30 آبان 1403، تاریخ پذیرش: 11 آذر 1403 | ||
| چکیده | ||
| A Roman dominating function on a graph $G = (V, E)$ is a function $f : V(G) → {0, 1, 2}$ satisfying the condition that every vertex u for which $f(u) = 0$ is adjacent to at least one vertex v for which $f(v) = 2$. The weight of a Roman dominating function is the value $f(V) = \sum_{u∈V(G)}f(u)$. The minimum possible weight of a Roman dominating function on $G$ is called the Roman domination number of $G$ and is denoted by $\gamma_R(G)$. In this paper, and among some other results, we provide some bounds for the Roman domination number of the subdivision graph $S(G)$ of an arbitrary graph $G$. Also, we determine the exact value of $\gamma_R(S(G))$ when $G$ is $K_n$, $K_{r,s} or $K_{n_1,n_2,...,n_k}$. | ||
| کلیدواژه‌ها | ||
| Roman dominating function؛ bipartite graph؛ tree | ||
| مراجع | ||
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