The shortest cycle having the maximal number of coalition graphs Научная публикация
| Журнал |
Discrete Mathematics Letters
ISSN: 2664-2557 |
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| Вых. Данные | Год: 2024, Том: 14, Страницы: 21-26 Страниц : 6 DOI: 10.47443/dml.2024.111 | ||||
| Ключевые слова | cycle, coalition partition, coalition number | ||||
| Авторы |
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| Организации |
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Информация о финансировании (2)
| 1 | Институт математики им. С.Л. Соболева СО РАН | FWNF-2022-0017 |
| 2 |
Министерство науки и высшего образования РФ Математический центр в Академгородке |
075-15-2019-1613, 075-15-2022-281 |
Реферат:
A coalition in a graph G with a vertex set V consists of two disjoint sets V1, V2 ⊂ V , such that neither V1 nor V2 is a dominating set, but the union V1 ∪ V2 is a dominating set in G. A partition of V is called a coalition partition π if every non-dominating set of π is a member of a coalition and every dominating set is a single-vertex set. Every coalition partition generates its coalition graph. The vertices of the coalition graph correspond one-to-one with the partition sets and two vertices are adjacent if and only if their corresponding sets form a coalition. In the paper [T. W. Haynes, J. T. Hedetniemi, S. T. Hedetniemi, A. A. McRae, R. Mohan, Discuss. Math. Graph Theory 43 (2023) 931–946], the authors proved that partition coalitions of cycles can generate only 27 coalition graphs and asked about the shortest cycle having the maximum number of coalition graphs. In this paper, we show that C15 is the shortest graph having this property.
Библиографическая ссылка:
Dobrynin A.A.
, Golmohammadi H.
The shortest cycle having the maximal number of coalition graphs
Discrete Mathematics Letters. 2024. V.14. P.21-26. DOI: 10.47443/dml.2024.111 WOS Scopus РИНЦ OpenAlex
The shortest cycle having the maximal number of coalition graphs
Discrete Mathematics Letters. 2024. V.14. P.21-26. DOI: 10.47443/dml.2024.111 WOS Scopus РИНЦ OpenAlex
Даты:
| Поступила в редакцию: | 17 мая 2024 г. |
| Принята к публикации: | 17 июл. 2024 г. |
| Опубликована в печати: | 18 июл. 2024 г. |
| Опубликована online: | 18 июл. 2024 г. |
Идентификаторы БД:
| Web of science: | WOS:001281072900003 |
| Scopus: | 2-s2.0-85215625913 |
| РИНЦ: | 68881787 |
| OpenAlex: | W4400724644 |
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