A class of trees with equal broadcast and domination numbers
Christina M. Mynhardt, Jane Wodlinger · Australas. J Comb. · 2013
A broadcast on a graph G is a function f : V →{ 0, 1, 2 ,... }. The broadcast number of G is the minimum value ofv∈V f (v )a mong all broadcasts f for which each vertex of G is within distance f (v )f rom some vertex v with f (v) ≥ 1. The broadcast number is bounded above by the radius and the domination number of G. We consider a class of trees that contains the caterpillars and char- acterize the trees in this class that have equal domination and broad- cast numbers, thus generalizing the results in: (S. M. Seager, Dominating broadcasts of caterpillars, Ars Combin. 88 (2008), 307-319).