The Italian domination numbers of some products of directed cycles

07/26/2020

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by   Kijung Kim, et al.

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An Italian dominating function on a digraph D with vertex set V(D) is defined as a function f : V(D) →{0, 1, 2} such that every vertex v ∈ 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 the exact values of the Italian domination numbers of some products of directed cycles.