A new construction of broadcast graphs

Abstract

Given a graph G = (V,E) and an originator vertex v, broadcasting is an information disseminating process of transmitting a message from vertex v to all vertices of graph G as quickly as possible. A graph G on n vertices is called broadcast graph if the broadcasting from any vertex in the graph can be accomplished in [log n] time. A broadcast graph with the minimum number of edges is called minimum broadcast graphs. The number of edges in a minimum broadcast graph on n vertices is denoted by B(n). A long sequence of papers present different techniques to construct broadcast graphs and to obtain upper bounds on B(n). In this paper, we follow the compounding method to construct new broadcast graphs and improve the known upper bounds on B(n) for many values of n.