Email this article Complexity of discrete Seifert foliations over a graph
- Authors: Kwon Y.1, Mednykh A.D.2,3, Mednykh I.A.2,3
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Affiliations:
- Yeungnam University
- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 486, No 4 (2019)
- Pages: 411-415
- Section: Mathematics
- URL: https://journals.eco-vector.com/0869-5652/article/view/14417
- DOI: https://doi.org/10.31857/S0869-56524864411-415
- ID: 14417
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Abstract
In the present paper, we study the complexity of an infinite family of graphs Hn = Hn(G1, G2, ..., Gm) that are discrete Seifert foliations over a graph H on m vertices with fibers G1, G2, ..., Gm. Each fiber Gi = Cn(si,1, si,2, ..., si,ki) of this foliation is the circulant graph on n vertices with jumps si,1, si,2, ..., si,ki. The family of discrete Seifert foliations is sufficiently large. It includes the generalized Petersen graphs, I-graphs, Y-graphs, H-graphs, sandwiches of circulant graphs, discrete torus graph and others. We obtain a closed formula for the number t(n) of spanning trees in Hn in terms of Chebyshev polynomials, investigate some arithmetical properties of this function and find its asymptotics as n → ∞.
About the authors
Young Soo Kwon
Yeungnam University
Email: smedn@mail.ru
Korea, Republic of, 280 Daehak-ro, Joyeong-dong, Gyeongsan, Gyeongsangbuk-do
A. D. Mednykh
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Author for correspondence.
Email: smedn@mail.ru
Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090; 1, Pirogova street, Novosibirsk, 630090
I. A. Mednykh
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Email: smedn@mail.ru
Russian Federation, 4, Acad. Koptyug prospect, Novosibirsk, 630090; 1, Pirogova street, Novosibirsk, 630090
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