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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Mostafa Blidia
Department of Mathematics, University of Blida 1. B.P. 270, Blida, Algeria
Electrical & Electronics Engineering

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Roman domination in oriented trees Lyes Ouldrabah; Mostafa Blidia; Ahmed Bouchou
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 1 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.1.9

Abstract

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. 
Co-Authors Ahmed Bouchou Lyes Ouldrabah