Twin roman domination number of a digraph

Abstract

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 in-neighbor and out-neighbor with label 2. The weight of a TRDF f is the value ω(f)= Συ∈V(D)f(υ). The twin Roman domination number of a digraph D, denoted by γR*(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 γR*(D) and determine the exact value of the twin Roman domination number for some classes of digraphs.