Italian Domination of Cartesian Products of Directed Cycles

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.

6 pages