Roman domination in cartesian product graphs and strong product graphs

Abstract

A map f : V → {0, 1, 2} is a Roman dominating function for G if for every vertex v with f(v) = 0, there exists a vertex u, adjacent to v, with f(u) = 2. The weight of a Roman dominating function is f(V ) = ∑u∈V f(u). The minimum weight of a Roman dominating function on G is the Roman domination number of G. In this paper we study the Roman domination number of Cartesian product graphs and strong product graphs.