Broadcasts and domination in trees

A broadcast on a graph G is a function f : V → Z + ∪ { 0 } . The broadcast number of G is the minimum value of ∑ v ∈ V f ( v ) among all broadcasts f for which each vertex of G is within distance f ( v ) from some vertex v with f ( v ) ≥ 1 . This number is bounded above by the radius and the domination number of G . We show that to characterize trees with equal broadcast and domination numbers it is sufficient to characterize trees for which all three of these parameters coincide.