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Complexity of Discrete Seifert Foliations over a Graph. / Kwon, Young Soo; Mednykh, A. D.; Mednykh, I. A.
в: Doklady Mathematics, Том 99, № 3, 01.05.2019, стр. 286-289.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Complexity of Discrete Seifert Foliations over a Graph
AU - Kwon, Young Soo
AU - Mednykh, A. D.
AU - Mednykh, I. A.
N1 - Publisher Copyright: © 2019, Pleiades Publishing, Ltd.
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