Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
419323 | Discrete Applied Mathematics | 2014 | 6 Pages |
A broadcast graph is a connected graph, G=(V,E)G=(V,E), |V|=n|V|=n, in which each vertex can complete broadcasting of one message within at most t=⌈logn⌉t=⌈logn⌉ time units. A minimum broadcast graph on nn vertices is a broadcast graph with the minimum number of edges over all broadcast graphs on nn vertices. The cardinality of the edge set of such a graph is denoted by B(n)B(n). In this paper we construct a new broadcast graph with B(n)≤(k+1)N−(t−k2+2)2k+t−k+2, for n=N=(2k−1)2t+1−kn=N=(2k−1)2t+1−k and B(n)≤(k+1−p)n−(t−k2+p+2)2k+t−k−(p−2)2p, for 2t