(untitled) (Journal of Informatics and Mathematical Sciences, 2017)
A function \(f : V→[0, 1, 2]\) is said to be Roman dominating function on a graph \(G=(V, E)\) if the function \(f\) satisfies the condition that every vertex \(u\) for which \(f(u)=0\) has at least one neighboring vertex \(v\) with \(f(v)=2\). The weight of a Roman dominating function is the value \(f(V)=_vVf(v)\). The Roman domination number of \(G\) is the minimum weight of a Roman dominating function and is denoted by \(γ_R(G)\). In this paper we study the Roman domination number on acyclic permutation graphs.