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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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[1] H. Abdollahzadeh Ahangar, M. Chellali, M. Hajjari, and S.M. Sheikholeslami, Further progress on the total Roman $\{2\}$-domination number of graphs, Bull. Iranian Math. Soc. 48 (2022), no. 3, 1111–1119. https://doi.org/10.1007/s41980-021-00565-z
[2] H. Abdollahzadeh Ahangar, M. Chellali, S.M. Sheikholeslami, and J.C. Valenzuela-Tripodoro, Total Roman $\{2\}$-dominating functions in graphs, Discuss. Math. Graph Theory 42 (2024), no. 3, 937–958. https://doi.org/10.7151/dmgt.2316
[3] S. Banerjee, M.A. Henning, and D. Pradhan, Perfect Italian domination in cographs, Appl. Math. Comput. 391 (2021), 125703. https://doi.org/10.1016/j.amc.2020.125703
[4] A. Cabrera-Martínez, A. Conchado Peiró, and J.M. Rueda-Vázquez, Further results on the total Italian domination number of trees, AIMS Math. 8 (2023), no. 5, 10654–10664. https://doi.org/10.3934/math.2023540
[5] M. Chellali, T.W. Haynes, S.T. Hedetniemi, and A.A. McRae, Roman $\{2\}$-domination, Discrete Appl. Math. 204 (2016), 22–28. https://doi.org/10.1016/j.dam.2015.11.013
[6] G. Hao, K. Hu, S. Wei, and Z. Xu, Global Italian domination in graphs, Quaest. Math. 42 (2019), no. 8, 1101–1115. https://doi.org/10.2989/16073606.2018.1506831 [7] Z. Liang, L. Wu, and J. Yang, The Italian domination numbers of some generalized Sierpiński networks, Discrete Math. Algorithms Appl. 16 (2024), no. 4, 2350045. https://doi.org/10.1142/S1793830923500453
[8] J. Lyle, Regular graphs with large Italian domatic number, Commun. Comb. Optim. 7 (2022), no. 2, 257–271. https://doi.org/10.22049/CCO.2021.27092.1194
[9] K. Paul and A. Pandey, Perfect Italian domination on some generalizations of cographs, Comp. Appl. Math. 43 (2024), no. 6, Article number: 390. https://doi.org/10.1007/s40314-024-02901-5
[10] D. Pradhan, S. Banerjee, and J.B. Liu, Perfect Italian domination in graphs: Complexity and algorithms, Discrete Appl. Math. 319 (2022), 271–295. https://doi.org/10.1016/j.dam.2021.08.020
[11] L. Volkmann, Remarks on the restrained Italian domination number in graphs, Commun. Comb. Optim. 8 (2023), no. 1, 183–191. https://doi.org/10.22049/CCO.2021.27471.1269 | ||
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