On the global Italian domination of graphs

Document Type : Original paper

Authors

1 School of Mathematics and Statistics, Heze University, Heze 274015, Shandong, China

2 School of Business, Heze University, Heze 274015, Shandong, China

3 School of Computer Information Engineering, Nanchang Institute of Technology, Nanchang 330044, Jiangxi, P.R. China

4 Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran

Abstract

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.

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Main Subjects

References

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Communications in Combinatorics and Optimization
Volume 11, Issue 4
Special issue in honor of Prof. Odile Favaron
December 2026
Pages 1141-1155

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