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On the global Italian domination of graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 7، دوره 11، شماره 4، اسفند 2026، صفحه 1141-1155 اصل مقاله (454.96 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30937.2670 | ||
| نویسندگان | ||
| Guoliang Hao1؛ Zhihong Xie* 2؛ Yuqi Wu3؛ Seyed Mahmoud Sheikholeslami* 4 | ||
| 1School of Mathematics and Statistics, Heze University, Heze 274015, Shandong, China | ||
| 2School of Business, Heze University, Heze 274015, Shandong, China | ||
| 3School of Computer Information Engineering, Nanchang Institute of Technology, Nanchang 330044, Jiangxi, P.R. China | ||
| 4Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Italian domination؛ global Italian domination؛ cubic graph | ||
| مراجع | ||
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