On domination and reinforcement numbers in trees

The reinforcement number of a graph is the smallest number of edges that have to be added to a graph to reduce the domination number. We introduce the k-reinforcement number of a graph as the smallest number of edges that have to be added to a graph to reduce the domination number by k. We present an O(k2 n) dynamic programming algorithm for computing the maximum number of vertices that can be dominated using (G) - k dominators for trees. A corollary of this is a linear-time algorithm for computing the k-reinforcement number of a tree. We also discuss extensions and related problems. Key Words: Domination, Reinforcement, Trees

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Jean R. S. Blair, Wayne Goddard, Stephen T. Hedetniemi, Steve Horton, Patrick Jones, Grzegorz Kubicki
• Keywords: DM 2008, Domination Number, K-reinforcement Number, Smallest Number