Given a graph G=(V,E), a function f:V\rightarrow \{0,1,2,3\} having the property that if f(v)=0, then there exist v_{1},v_{2}\in N(v) such that f(v_{1})=2=f(v_{2}) or there
exists w \in N(v) such that f(w)=3, and if f(v)=1, then there exists w \in N(v) such that f(w)\geq 2 is called a double Roman dominating function (DRDF). The weight of a DRDF f is
the sum f(V)=\sum_{v\in V}f(v), and the minimum among the weights of DRDFs on G is the double Roman domination number, \gamma_{dR}(G), of G. In this paper, we study the impact of cartesian product on the double Roman domination number.

 

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Author(s)

Anu, V., Aparna, Lakshmanan S.