The number of rooted forests in circulant graphs Научная публикация
| Журнал |
Ars Mathematica Contemporanea
ISSN: 1855-3966 , E-ISSN: 1855-3974 |
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| Вых. Данные | Год: 2022, Том: 22, Номер: 4, Номер статьи : #P4.10, Страниц : DOI: 10.26493/1855-3974.2029.01d | ||||
| Ключевые слова | Chebyshev polynomial; circulant graph; Laplacian matrix; Mahler measure; Rooted tree; spanning forest | ||||
| Авторы |
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| Организации |
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Информация о финансировании (1)
| 1 |
Министерство науки и высшего образования РФ Математический центр в Академгородке |
075-15-2019-1613, 075-15-2022-281 |
Реферат:
In this paper, we develop a new method to produce explicit formulas for the number fG(n) of rooted spanning forests in the circulant graphs G = Cn(s1, s2, ..., sk) and G = C2n(s1, s2, ..., sk, n). These formulas are expressed through Chebyshev polynomials. We prove that in both cases the number of rooted spanning forests can be represented in the form fG(n) = p a(n)2, where a(n) is an integer sequence and p is a certain natural number depending on the parity of n. Finally, we find an asymptotic formula for fG(n) through the Mahler measure of the associated Laurent polynomial P(z) = 2k+1−Σki=1(zsi +z−si). © 2022 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.
Библиографическая ссылка:
Grunwald L.A.
, Mednykh I.
The number of rooted forests in circulant graphs
Ars Mathematica Contemporanea. 2022. V.22. N4. #P4.10 . DOI: 10.26493/1855-3974.2029.01d WOS Scopus РИНЦ OpenAlex
The number of rooted forests in circulant graphs
Ars Mathematica Contemporanea. 2022. V.22. N4. #P4.10 . DOI: 10.26493/1855-3974.2029.01d WOS Scopus РИНЦ OpenAlex
Идентификаторы БД:
| Web of science: | WOS:000898437800010 |
| Scopus: | 2-s2.0-85138637459 |
| РИНЦ: | 56379392 |
| OpenAlex: | W2954392891 |