broadcast domination in tori

A broadcast on a graph g is a function f : v (g) → {0, 1, . . . , diam(g)} such that for every vertex v ∈ v (g), f (v) ≤ 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 σ(f ) = ∑v∈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 cm □ cn.