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The number of rooted forests in circulant graphs. / Grunwald, Lilya A.; Mednykh, Ilya.

In: Ars Mathematica Contemporanea, Vol. 22, No. 4, #P4.10, 2022.

Research output: Contribution to journal › Article › peer-review

Harvard

Grunwald, LA & Mednykh, I 2022, 'The number of rooted forests in circulant graphs', Ars Mathematica Contemporanea, vol. 22, no. 4, #P4.10. https://doi.org/10.26493/1855-3974.2029.01d

APA

Grunwald, L. A., & Mednykh, I. (2022). The number of rooted forests in circulant graphs. Ars Mathematica Contemporanea, 22(4), [#P4.10]. https://doi.org/10.26493/1855-3974.2029.01d

Vancouver

Grunwald LA, Mednykh I. The number of rooted forests in circulant graphs. Ars Mathematica Contemporanea. 2022;22(4):#P4.10. doi: 10.26493/1855-3974.2029.01d

Author

Grunwald, Lilya A. ; Mednykh, Ilya. / The number of rooted forests in circulant graphs. In: Ars Mathematica Contemporanea. 2022 ; Vol. 22, No. 4.

BibTeX

@article{0f8afc47d9654f0f87086df8995867cc,
title = "The number of rooted forests in circulant graphs",
abstract = "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).",
keywords = "Chebyshev polynomial, circulant graph, Laplacian matrix, Mahler measure, Rooted tree, spanning forest",
author = "Grunwald, {Lilya A.} and Ilya Mednykh",
note = "Funding Information: *The authors are grateful to all the three anonymous referees for careful reading of manuscript and valuable remarks and suggestions. The authors were supported by the Mathematical Center in Akademgorodok, agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. †Corresponding author. E-mail addresses: lfb o@yahoo.co.uk (Lilya A. Grunwald), ilyamednykh@mail.ru (Ilya Mednykh) Publisher Copyright: {\textcopyright} 2022 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.",
year = "2022",
doi = "10.26493/1855-3974.2029.01d",
language = "English",
volume = "22",
journal = "Ars Mathematica Contemporanea",
issn = "1855-3966",
publisher = "DMFA Slovenije",
number = "4",

}

RIS

TY - JOUR

T1 - The number of rooted forests in circulant graphs

AU - Grunwald, Lilya A.

AU - Mednykh, Ilya

N1 - Funding Information: *The authors are grateful to all the three anonymous referees for careful reading of manuscript and valuable remarks and suggestions. The authors were supported by the Mathematical Center in Akademgorodok, agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. †Corresponding author. E-mail addresses: lfb o@yahoo.co.uk (Lilya A. Grunwald), ilyamednykh@mail.ru (Ilya Mednykh) Publisher Copyright: © 2022 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.

PY - 2022

Y1 - 2022

N2 - 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).

AB - 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).

KW - Chebyshev polynomial

KW - circulant graph

KW - Laplacian matrix

KW - Mahler measure

KW - Rooted tree

KW - spanning forest

UR - http://www.scopus.com/inward/record.url?scp=85138637459&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.2029.01d

DO - 10.26493/1855-3974.2029.01d

M3 - Article

AN - SCOPUS:85138637459

VL - 22

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 4

M1 - #P4.10

ER -

ID: 38048377