University of IsfahanTransactions on Combinatorics2251-86574420151201Broadcast domination in Tori4353765410.22108/toc.2015.7654ENKian WeeSohDept of Mathematics, National University of SingaporeKhee-MengKohDepartment of Mathematics
National University of SingaporeJournal Article20141021A <em>broadcast</em> 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 <em>dominating broadcast</em>. The <em>cost</em> 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 <em>broadcast domination number</em>) for a torus $C_{m} \;\Box\; C_{n}$.https://toc.ui.ac.ir/article_7654_d69d40ef7aab331d7b142121c88012e9.pdf