A double Roman Dominating function on a graph G is a function f:V(G)→{0,1,2,3} such that the following conditions hold. If f(v)=0, then vertex v must have at least two neighbors in V_2 or one neighbor in V_3 and if f(v)=1, then vertex v must have at least one neighbor in V_2⋃V_3. The weight of a double Roman dominating function f is the sum ω(f)=∑_(v∈V(G))〖f(v)〗. In this paper, we obtain the upper bounds for γ_dR (G), for any graph with δ(G)≥2.
