Restrained bondage in graphs

Let G = (V, E) be a graph. A set S V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V - S. The restrained domination number of G, denoted by r(G), is the smallest cardinality of a restrained dominating set of G. We define the restrained bondage number br(G) of a nonempty graph G to be the minimum cardinality among all sets of edges E E for which r(G - E ) > r(G). Sharp bounds are obtained for br(G), and exact values are determined for several classes of graphs. Also, we show that the decision problem for br(G) is NP-complete even for bipartite graphs.

• Type: Journal
• Year: 2008
• Where: DM
• Authors: Johannes H. Hattingh, Andrew R. Plummer
• Keywords: DM 2008, Dominating Set, Restrained Bondage Number, Restrained Domination Number