A broadcast on a graph G=(V,E) is a function f : V → {0, ..., diam(G)} that assigns an integer value to each vertex such that, for each v ∈ V , f (v) ≤ e(v), the eccentricity of v. The broadcast number of a graph is the minimum value of Σv∈V f (v) among all broadcasts f with the property that for each vertex x of V, f (v) ≥ d(x, v) for some vertex v having positive f (v). This number is bounded above by both the radius of the graph and its domination number. Graphs for which the broadcast number is equal to the domination number are called 1-cap graphs. We investigate and characterize a class of 1-cap trees. / Graduate