Reinforcement numbers of digraphs

Authors:
Jia Huang;Jian-Wei Wang;Jun-Ming Xu
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

The reinforcement number of a graph G is the minimum cardinality of a set of extra edges whose addition results in a graph with domination number less than the domination number of G. In this paper we consider this parameter for digraphs, investigate the relationship between reinforcement numbers of undirected graphs and digraphs, and obtain further results for regular graphs. We also determine the exact values of the reinforcement numbers of de Bruijn digraphs and Kautz digraphs.