Time Bound for Broadcasting in Bounded Degree Graphs

Broadcasting is the process of transmitting a message from a node to all other nodes in a network. The problem of constructing sparse graphs in which the broadcast could be accomplished in minimum time has been investigated in several papers. However, the proposed graphs may have nodes of high degree that could be unacceptable from a network designer's point of view. In this paper we consider the problem of broadcasting on bounded degree graphs. We provide a lower bound on the time necessary to accomplish the broadcast when the maximum node degree is fixed. Moreover, we propose a method to construct bounded degree graphs in which the time to complete the broadcast from any node is of the same order as the lower bound. We also obtain the only known families of graphs having exactly minimum broadcast time.