The Italian domination numbers of some products of directed cycles

TL;DR

This paper determines the exact Italian domination numbers for certain products of directed cycles, expanding understanding of domination parameters in directed graph products.

Contribution

It provides new exact values for Italian domination numbers in specific directed cycle product graphs, a previously unexplored area.

Findings

Exact Italian domination numbers for some directed cycle products are established.

The results contribute to the theory of domination in directed graph products.

Abstract

An Italian dominating function on a digraph $D$ with vertex set $V(D)$ is defined 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 the exact values of the Italian domination numbers of some products of directed cycles.