An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree Original Research Article

Let image be a graph. A set image is a restrained dominating set if every vertex in image is adjacent to a vertex in image and to a vertex in image. The restrained domination number of image, denoted image, is the smallest cardinality of a restrained dominating set of image. We will show that if image is a connected graph of order image and minimum degree image and not isomorphic to one of nine exceptional graphs, then image.