Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 11 4 2026 12 01 On the global Italian domination of graphs 1141 1155 15075 10.22049/cco.2025.30937.2670 EN Guoliang Hao School of Mathematics and Statistics, Heze University, Heze 274015, Shandong, China Zhihong Xie School of Business, Heze University, Heze 274015, Shandong, China Yuqi Wu School of Computer Information Engineering, Nanchang Institute of Technology, Nanchang 330044, Jiangxi, P.R. China Seyed Mahmoud Sheikholeslami Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran Journal Article 2025 08 24 Let $H$ be a graph with vertex set $V.$ An Italian dominating function (IDF) on $H$ is a function from $V$ to the set $\{0,1,2\}$ having the property that any vertex assigned $0$ is adjacent to two vertices assigned $1$ or one vertex assigned $2.$ The value $\sum_{x\in V}h(x)$ is called the weight of an IDF $h$ on $H.$ A global Italian dominating function (GIDF) on $H$ is an IDF on $H$ and its complement. The minimum weight of an IDF (resp., GIDF) on $H$ is the Italian (resp., global Italian) domination number of $H.$ In this paper, we establish several relations between the global Italian domination and Italian domination numbers. In particular, we determine the difference between these two parameters of cubic graphs. https://comb-opt.azaruniv.ac.ir/article_15075_0c701829ef369cf9cc1ed36488cfa4cd.pdf