Restrained domination in trees

AbstractLet 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 γr(G), is the smallest cardinality of a restrained dominating set of G. We show that if T is a tree of order n, then γr(T)⩾⌈(n+2)/3⌉. Moreover, we constructively characterize the extremal trees T of order n achieving this lower bound