Abstract

Compound methods have been shown to be very effective in the construction of broadcast graphs. Compound methods generate a large broadcast graph by combining multiple copies of a broadcast graph $G$ using the structure of another broadcast graph $H$. Node deletion is also allowed in some of these methods. The subset of connecting nodes of $G$ has been defined as solid $h$-cover by Bermond, Fraigniaud and Peters, and center node set by Weng and Ventura. This article shows that the two concepts are equivalent. We also provide new properties for center node sets, including bounds on the minimum size of a center node set, show how to reduce the number of center nodes of a broadcast graph generated by a compound method, and propose an iterative compounding algorithm that generates the sparsest known broadcast graphs in many cases.