• STRONG ROMAN DOMINATION IN GRAPHS

Abstract

A Roman dominating function on a graph G = (V; E) is a function f: V → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2: The weight of a  Roman dominating function is the value f(V) =. The minimum weight of a Roman dominating function on a graph G is called the Roman dominating number of G: In this paper, we introduced the concept of strong Roman domination which is the generalization of Roman domination and we study the graph theoretic properties of this variant of the domination number of a graph.