مشخصات پژوهش

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 W V.D/ ! f0; 1;2g such that every vertex with label 0 has a in-neighbor and out-neighbor with label 2. The weight of a TRDF f is the value !.f / D Pv2V.D/ f .v/. The twin Roman domination number of a digraph D, denoted by 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 R .D/ and determine the exact value of the twin Roman domination number for some classes of digraphs.