Italian Domination of Cartesian Products of Directed Cycles

TL;DR

This paper investigates the Italian domination numbers of Cartesian products of directed cycles, providing a comprehensive analysis of their properties and values.

Contribution

It completes the study of Italian domination numbers specifically for Cartesian products of directed cycles, filling a gap in graph domination theory.

Findings

Determined the Italian domination numbers for Cartesian products of directed cycles.

Provided formulas or bounds for these domination numbers.

Enhanced understanding of domination properties in directed graph products.

Abstract

An Italian dominating function on a (di)graph $G$ with vertex set $V(G)$ is a function $f: V(G) \to \{0, 1, 2\}$ such that every vertex $v \in V(G)$ such that $f(v) = 0$ has an (in)neighbour assigned 2 or two (in)neighbours assigned 1. We complete the investigation of the Italian domination numbers of Cartesian products of directed cycles.