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چکیده
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A {\em double Roman dominating function} (DRDF) on a graph $G=(V,E)$ is a function $f:V(G)\rightarrow\{0,1,2,3\}$ having the property that if $f(v)=0$, then vertex $v$ have at least two neighbors assigned 2 under $f$ or one neighbor $w$ with $f(w)=3$, and if $f(v)=1$, then vertex $v$ must have at leat one neighbor $w$ with $f(w)\ge 2$. The weight of a DRDF is the value $f(V(G))=\sum_{u\in V(G)}f(u).$ The \textit{double Roman domination number} $\gamma_{dR}(G)$ is the minimum weight of a DRDF on $G$. Graphs which have double Roman domination number equals to thrice their domination number are called double Roman graphs.
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