Restrained domination in unicyclic graphs

Let G = (V,E) be a graph. A set S ⊆ V is a restrained dominating set if every vertex in V - S is adjacent to a vertex in S and to a vertex in V - S. The restrained domination number of G, denoted by yr(G), is the minimum cardinality of a restrained dominating set of G. A unicyclic graph is a connected graph that contains precisely one cycle. We show that if U is a unicyclic graph of order n, then yr(U) ≥ d n 3 e, and provide a characterization of graphs achieving this bound.