Some sparse time-relaxed broadcast communication networks

Broadcasting is the process of information dissemination in communication networks (modelled as graphs) whereby a message originated at one vertex becomes known to all members under the constraints that each call requires one unit of time and at every step any member can call at most one of its neighbours. A broadcast graph on n vertices is a network in which message can be broadcast in minimum possible (=[log₂n]) time regardless of originator. Broadcast graphs having the smallest number of edges are called Minimum Broadcast Graphs, and are subject of intensive study. On the other hand, in Shastri (1995) we have considered how quickly broadcasting can be done in trees. In this paper, we construct more and more sparse time-relaxed broadcast graphs for some small values of n, as we allow additional time over [log ₂n], until we get a tree