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Abstract
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A double Roman dominating function (DRDF) on a graph G=(V, E) is a function f : V(G) ----{0, 1, 2, 3} having the property that f(v)=0, then vertex v must have at least two beighbors assigned 2 under f or one neighbor w with f(w)=3, and if f(v)=1, then vertex v must have at least one neighbor w with f(w)>2. The weight of a DRDF is the value f(V(G))=sigma f(u). The double Roman domination number is the minimum weight of a DRDF on G.
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