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∈Vf(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.