## Abstract

Abstract: We study the complexity of an infinite family of graphs H_{n}=H_{n} (G_{1},G_{2},...,G_{m}) that are discrete Seifert foliations over a given graph H on m vertices with fibers G_{1},G_{2},...,G_{m}. Each fiber G_{i} = C_{n}(S_{i,1},S_{i,2},...,S_{i,ki}) of this foliation is a circulant graph on n vertices with jumps S_{i,1},S_{i,2},...,S_{i,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 H_{n} is obtained in terms of Chebyshev polynomials, some analytical and arithmetic properties of this function are investigated, and its asymptotics as n → ∞ is determined.

Original language | English |
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Pages (from-to) | 286-289 |

Number of pages | 4 |

Journal | Doklady Mathematics |

Volume | 99 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2019 |

## Keywords

- COUNTING SPANNING-TREES