Let G = (V, E) be a simple graph. A double Roman dominating function of a graph G is a function {0,1,2,3} : V f having the property that if 0 = ) (v f , then the vertex v must have at least two neighbors 1 w , 2w such that 2 = ) ( = ) ( 1 2 w f w f or one neighbor w such that 3 = ) (w f ; and if 1=) (v f , then the vertex v must have at least one neighbor w such that f (w) 2 . The weight of a double Roman dominating function is the sum = ( ) ( ) w f v f v V G , and the minimum weight of f w for every double Roman dominating function f on G is called double Roman domination number of G . We denote this number with ) (G dR . In this paper; we obtain some new lower and upper bounds of double Roman domination number of graphs.
