Broadcast domination in Tori

A broadcast on a graph G is a function f‎ : ‎V(G) \rightarrow \{۰‎, ‎۱,\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}‎.