On the global Italian domination of graphs

Articles in Press

Document Type : Special issue of CCO to honor Odile Favaron

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.

Keywords

Main Subjects

References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 16 December 2025

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