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An Italian dominating function on a digraph $D$ with vertex set $V(D)$ isdefined as a function $f : V(D) \rightarrow \{0, 1, 2\}$ such that every vertex$v \in V(D)$ with $f(v) = 0$ has at least two in-neighbors assigned $1$ under$f$ or one in-neighbor $w$ with $f(w) = 2$. In this paper, we determine theexact values of the Italian domination numbers of some products of directedcycles.

The Italian domination numbers of some products of directed cycles