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Broadcast domination in Tori | ||
| Transactions on Combinatorics | ||
| مقاله 5، دوره 4، شماره 4، اسفند 2015، صفحه 43-53 اصل مقاله (273.53 K) | ||
| نوع مقاله: 75th Birthday of G. B. Khosrovshahi | ||
| شناسه دیجیتال (DOI): 10.22108/toc.2015.7654 | ||
| نویسندگان | ||
| Kian Wee Soh1؛ Khee-Meng Koh* 2 | ||
| 1Dept of Mathematics, National University of Singapore | ||
| 2Department of Mathematics National University of Singapore | ||
| چکیده | ||
| A broadcast on a graph $G$ is a function $f : V(G) \rightarrow \{0, 1,\dots, diam(G)\}$ such that for every vertex $v \in V(G)$, $f(v) \leq e(v)$, where $diam(G)$ is the diameter of $G$, and $e(v)$ is the eccentricity of $v$. In addition, if every vertex hears the broadcast, then the broadcast is a dominating broadcast. The cost of a broadcast $f$ is the value $\sigma(f) = \sum_{v \in V(G)} f(v)$. In this paper we determine the minimum cost of a dominating broadcast (also known as the broadcast domination number) for a torus $C_{m} \;\Box\; C_{n}$. | ||
| کلیدواژه‌ها | ||
| Broadcast؛ Dominating broadcast؛ Broadcast domination؛ Torus؛ Radial graph | ||
| مراجع | ||
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D. Erwin (2004) Dominating broadcasts in graph Bull. Inst. Comb. Appl. 42, 89-105
J. Dunbar, D. Erwin, T. Haynes, S. M. Hedetniemi and S. T. Hedetniemi (2006) Broadcasts in graphs Discrete Appl. Math. 154, 59-75
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