Complexity of Discrete Seifert Foliations over a Graph

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Complexity of Discrete Seifert Foliations over a Graph. / Kwon, Young Soo; Mednykh, A. D.; Mednykh, I. A.

In: Doklady Mathematics, Vol. 99, No. 3, 01.05.2019, p. 286-289.

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

Harvard

Kwon, YS, Mednykh, AD & Mednykh, IA 2019, 'Complexity of Discrete Seifert Foliations over a Graph', Doklady Mathematics, vol. 99, no. 3, pp. 286-289. https://doi.org/10.1134/S1064562419030141

APA

Kwon, Y. S., Mednykh, A. D., & Mednykh, I. A. (2019). Complexity of Discrete Seifert Foliations over a Graph. Doklady Mathematics, 99(3), 286-289. https://doi.org/10.1134/S1064562419030141

Vancouver

Kwon YS, Mednykh AD , Mednykh IA. Complexity of Discrete Seifert Foliations over a Graph. Doklady Mathematics. 2019 May 1;99(3):286-289. doi: 10.1134/S1064562419030141

Author

Kwon, Young Soo ; Mednykh, A. D. ; Mednykh, I. A. / Complexity of Discrete Seifert Foliations over a Graph. In: Doklady Mathematics. 2019 ; Vol. 99, No. 3. pp. 286-289.

BibTeX

@article{78292b06655b4076b8760dbb36e45c6f,

title = "Complexity of Discrete Seifert Foliations over a Graph",

abstract = "Abstract: We study the complexity of an infinite family of graphs Hn=Hn (G1,G2,...,Gm) that are discrete Seifert foliations over a given graph H on m vertices with fibers G1,G2,...,Gm. Each fiber Gi = Cn(Si,1,Si,2,...,Si,ki) of this foliation is a 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 graphs, and other graphs. A closed-form formula for the number τ(n) of spanning trees in Hn is obtained in terms of Chebyshev polynomials, some analytical and arithmetic properties of this function are investigated, and its asymptotics as n → ∞ is determined.",

keywords = "COUNTING SPANNING-TREES",

author = "Kwon, {Young Soo} and Mednykh, {A. D.} and Mednykh, {I. A.}",

note = "Publisher Copyright: {\textcopyright} 2019, Pleiades Publishing, Ltd.",

year = "2019",

month = may,

day = "1",

doi = "10.1134/S1064562419030141",

language = "English",

volume = "99",

pages = "286--289",

journal = "Doklady Mathematics",

issn = "1064-5624",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "3",

}

RIS

TY - JOUR

T1 - Complexity of Discrete Seifert Foliations over a Graph

AU - Kwon, Young Soo

AU - Mednykh, A. D.

AU - Mednykh, I. A.

PY - 2019/5/1

Y1 - 2019/5/1

N2 - Abstract: We study the complexity of an infinite family of graphs Hn=Hn (G1,G2,...,Gm) that are discrete Seifert foliations over a given graph H on m vertices with fibers G1,G2,...,Gm. Each fiber Gi = Cn(Si,1,Si,2,...,Si,ki) of this foliation is a 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 graphs, and other graphs. A closed-form formula for the number τ(n) of spanning trees in Hn is obtained in terms of Chebyshev polynomials, some analytical and arithmetic properties of this function are investigated, and its asymptotics as n → ∞ is determined.

AB - Abstract: We study the complexity of an infinite family of graphs Hn=Hn (G1,G2,...,Gm) that are discrete Seifert foliations over a given graph H on m vertices with fibers G1,G2,...,Gm. Each fiber Gi = Cn(Si,1,Si,2,...,Si,ki) of this foliation is a 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 graphs, and other graphs. A closed-form formula for the number τ(n) of spanning trees in Hn is obtained in terms of Chebyshev polynomials, some analytical and arithmetic properties of this function are investigated, and its asymptotics as n → ∞ is determined.

KW - COUNTING SPANNING-TREES

UR - http://www.scopus.com/inward/record.url?scp=85070019788&partnerID=8YFLogxK

U2 - 10.1134/S1064562419030141

DO - 10.1134/S1064562419030141

M3 - Article

AN - SCOPUS:85070019788

VL - 99

SP - 286

EP - 289

JO - Doklady Mathematics

JF - Doklady Mathematics

SN - 1064-5624

IS - 3

ER -

ID: 21144649