Abstract
AbstractThe term k‐broadcast indicates the process of disseminating a message from one vertex to all vertices of a graph in such a way that in each time unit, an informed vertex can send the message to up to k of its neighbors. The k‐broadcast center of a graph is the set of vertices that can initiate a minimum time k‐broadcast within the graph. We present a linear algorithm to determine the k‐broadcast center of a given tree. From this, we obtain a linear time algorithm for finding the k‐broadcast time of any vertex of the tree and, thus, the k‐broadcast time of the tree itself. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009
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