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

Let G=(V,E)G=(V,E) be a graph. A set S⊆VS⊆V is a restrained dominating set if every vertex in V−SV−S is adjacent to a vertex in SS and to a vertex in V−SV−S. The restrained domination number of GG, denoted γr(G)γr(G), is the smallest cardinality of a restrained dominating set of GG. We will show that if GG is a connected graph of order nn and minimum degree δδ and not isomorphic to one of nine exceptional graphs, then γr(G)≤n−δ+12.