A Minor Problem On Roman Domination In A Tree

A Roman domination function on a graph G = (V, E) is a function f : V→{0,1,2} satisfying the condition that every vertex in V₀ is adjacentto at least one vertex in V₂, where i=0,1,2, V_i = {μ: f(u) = i}. For each S (?) V, we define f(S) =∑_v∈S f(v), The weight of a Roman dominationfunction is the valueω(f) =∑_v∈Vf(v), The minimum weight of a Roman domination function on a graph G, denoted _γr(G), is called the Roman domination number of G, If T is a tree on two or more vertices ,then _γr(T) =_γ(T) + 1if and only if T is a wounded spider .In this paper , We study the properties of T with _γR(T) = _γ(T) + 2 and B(T)∩C(T)≠(?).