Open AccessComplexity of discrete Seifert foliations over a graph
Author(s) -
Young Soo Kwon,
Alexander Mednykh,
И. А. Медных
Publication year - 2019
Publication title -
doklady akademii nauk. rossijskaâ akademiâ nauk
Language(s) - English
Resource type - Journals
ISSN - 0869-5652
DOI - 10.31857/s0869-56524864411-415
Subject(s) - circulant matrix , mathematics , combinatorics , bipartite graph , chebyshev polynomials , arithmetic function , discrete mathematics , graph , mathematical analysis
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 → ∞.