Restrained bondage in graphs Original Research Article

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