Roman domination in oriented trees

Let D = (V, A) be a digraph of order n = vertical bar V vertical bar. A Roman dominating function of a digraph D is a function f : V -> {0, 1, 2} such that every vertex a for which f (u) = 0 has an in- neighbor v for which f (v) = 2. The weight of a Roman dominating function is the value f (V) = Sigma(u is an element of v) f (u). The minimum weight of a Roman dominating function of a digraph D is called the Roman domination number of D, denoted by gamma(R) (D). In this paper, we characterize oriented trees T satisfying gamma(R) (T) + Delta(+) (T) = n + 1.