New upper bound on m-time-relaxed k-broadcast graphs

Broadcasting is a process in which an individual has an item of information which needs to be transmitted to all of the members in a network (which is viewed as a connected graph). k-broadcasting is a variant of broadcasting in which each processor can transmit the message to up to k of its neighbors. Another variant of broadcasting is the concept of m-time-relaxed broadcasting, where we allow m additional time units, enabling one to decrease the number of edges in the communication network. The combination of m-time-relaxed and k-broadcasting is studied in this article. The results shown here are an improvement on the upper bound obtained by Harutyunyan and Liestman, Discrete Math 262 (2003), 149–157, by constructing a connected graph, which admits m-time-relaxed k-broadcasting for all n, and has fewer edges than the graph presented in Harutyunyan and Liestman, Discrete Math 262 (2003), 149–157.