Roman domination in oriented trees

Lyes Ouldrabah (Department of Mathematics, University of Blida 1. B.P. 270, Blida, Algeria)
Mostafa Blidia (Department of Mathematics, University of Blida 1. B.P. 270, Blida, Algeria)
Ahmed Bouchou (Department of Mathematics, University of Medea, Algeria)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications

Let D=(V,A) be a digraph of order n = |V|. A Roman dominating function of a digraph D is a function f : V  → {0,1,2} such that every vertex u 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)=∑u∈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 γR(D). In this paper, we characterize oriented trees T satisfying γR(T)+Δ+(T) = n+1.