The complexity of broadcasting in bounded-degree networks
  Broadcasting concerns the dissemination of a message originating at one node of a network to all other nodes. This task is accomplished by placing a series of calls over the communication lines of the network between neighboring nodes, where each call requires a unit of time and a call can involve only two nodes. We show that for bounded-degree networks determining the minimum broadcast time from an originating node remains NP-complete. 
Michael J. Dinneen