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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2601.12899 |
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Table des matières:
- A bi-Cayley graph over a cyclic group $\mathbb{Z}_n$ is called a bicirculant graph. Let $Γ=BC(\mathbb{Z}_n; R,T,S)$ be a bicirculant graph with $R=R^{-1}\subseteq \mathbb{Z}_n\setminus \{0\}$ and $T=T^{-1}\subseteq \mathbb{Z}_n\setminus \{0\}$ and $S\subseteq \mathbb{Z}_n$. In this paper, using Chebyshev polynomials, we obtain a closed formula for the number of spanning trees of bicirculant graph $Γ$, investigate some arithmetic properties of the number of spanning trees of $Γ$, and find its asymptotic behaviour as $n$ tends infinity. In addition, we show that $F(x)=\sum_{n=1}^{\infty}τ(Γ)x^n$ is a rational function with integer coefficients.