TWIN ROMAN DOMINATION NUMBER OF A DIGRAPH

Let D be a finite and simple digraph with vertex set V(D). A twin Roman dominating function (TRDF) on D is a labeling f : V(D) -> {0, 1, 2} such that every vertex with label 0 has an P in-neighbor and out-neighbor with label 2. The weight of a TRDF f is the value omega(f) = Sigma(v is an element of V(D)) f(v). The twin Roman domination number of a digraph D, denoted by gamma(R)*(D), equals the minimum weight of a TRDF on D. In this paper we initiate the study of the twin Roman domination number in digraphs. In particular, we present sharp bounds for gamma(R)*(D) and determine the exact value of the twin Roman domination number for some classes of digraphs.