Broadcasts in graphs

AbstractWe say that a function f:V→{0,1,…,diam(G)} is a broadcast if for every vertex v∈V, f(v)⩽e(v), where diam(G) denotes the diameter of G and e(v) denotes the eccentricity of v. The cost of a broadcast is the value f(V)=∑v∈Vf(v). In this paper we introduce and study the minimum and maximum costs of several types of broadcasts in graphs, including dominating, independent and efficient broadcasts