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 . The minimum weight of a Roman dominating function on a graph G, denoted byγR(G), is called the Roman dominating number of G. In this paper, we will characterize a tree T with γR(T) =γ(T) + 3.

Key words: Roman dominating function, Roman dominating number, dominating number, healthy spider, wounded spider