科研成果详情

Given a graph [Formula presented] and an originator vertex [Formula presented], broadcasting is an information disseminating process of transmitting a message from the vertex [Formula presented] to all vertices of the graph [Formula presented] as quickly as possible. A graph [Formula presented] on [Formula presented] vertices is called broadcast graph if the broadcasting from any vertex in the graph can be accomplished in [Formula presented] time. A broadcast graph with the minimum number of edges is called minimum broadcast graph. The number of edges in a minimum broadcast graph on [Formula presented] vertices is denoted by [Formula presented]. A long sequence of papers present different broadcast graph constructions and upper bounds on [Formula presented]. In this paper, we improve the compounding method and construct new broadcast graphs with a better upper bound on [Formula presented]. Consequently, we show that [Formula presented] for [Formula presented], where [Formula presented], [Formula presented], [Formula presented], [Formula presented], and [Formula presented].