Broadcast graphs using new dimensional broadcast schemes for Kn?del graphs

Broadcasting is an information disseminating process of distributing a message from an originator vertex v of graph G = (V, E) to all of its vertices. The broadcast time of vertex v is the minimum possible time required to broadcast from v in graph G. A graph G on n vertices is called broadcast graph if broadcasting from any originator in G can be accomplished in flog n right ceiling 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 n vertices is denoted by B(n). Finding the values of B(n) is very difficult. A large number of papers present techniques to construct broadcast graphs and to obtain upper bounds on B(n). In this paper, we first find new dimensional broadcast schemes for Knodel graphs (similar to the dimensions of hypercubes), and then use them to give a general upper bound on B(n) for almost all odd n.(c) 2023 Published by Elsevier B.V.