Gemmrich, L.Mynhardt, C.M.2017-08-212017-08-2120172017-08-21http://hdl.handle.net/1828/8436Accepted for publication in the Australasian Journal of CombinatoricsA dominating broadcast on a graph G=(V,E) is a function f:V→{0,1,…,diam(G)} such that f(v)≤e(v) (the eccentricity of v) for all v∈V, and each u∈V is at distance at most f(v) from a vertex v with f(v)≥1. The upper broadcast domination number of G is Γ_{b}(G)=max{∑_{v∈V}f(v):f is a minimal dominating broadcast on G}. As shown by Erwin in [D. Erwin, Cost domination in graphs, Doctoral dissertation, Western Michigan University, 2001], Γ_{b}(G)≥diam(G) for any graph G. We investigate trees whose upper broadcast domination number equal their diameter and, among more general results, characterise caterpillars with this property.enAttribution-NonCommercial-NoDerivs 2.5 Canadabroadcast on a graphdominating broadcastminimal dominating broadcastupper broadcast domination numberPostprint