Broadcast Domination in Graphs

For a graph G, a function f : V (G) →{0, 1, …, diam(G)} is a broadcast on G, where diam(G) denotes the diameter of G. For each vertex v in G, the value f(v) is the strength of the broadcast from v. For each vertex u ∈ V (G), if there exists a vertex v in G (possibly, u = v) such that f(v) > 0 and d(u, v) ≤ f(v), where d(u, v) is the distance betweenu and v, then f is called a dominating broadcast on G. The cost of the dominating broadcast f is the sum of the strengths of the broadcasts over all vertices in G, that is, the quantity ∑_{v ∈ V}f(v). The minimum cost of a dominating broadcast is the broadcast domination number of G. In this chapter, we survey selected results on the broadcast domination number of a graph.