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arXiv · 2512.19256

The number of rooted spanning forests of bicirculant graphs

Jing Yang·Lihua Feng·Rongrong Lu·Tingzeng Wu
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Abstract

A bi-Cayley graph over the cyclic group $(\mathbb{Z}_n, +)$ is called a bicirculant graph. Let $\Gamma=BC(\mathbb{Z}_n; R,T,S)$ be a bicirculant graph with $R=-R\subseteq \mathbb{Z}_n\setminus \{0\}$ and $T={-}T\subseteq \mathbb{Z}_n\setminus \{0\}$ and $S\subseteq \mathbb{Z}_n$. In this paper, using Chebyshev polynomials, we obtain a closed formula for the number of rooted spanning forests of $\Gamma$. Moreover, we investigate some arithmetic properties of the number of rooted spanning forests of $\Gamma$, and find its asymptotic behaviour as $n$ tends infinity.

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Jing Yang, Lihua Feng, Rongrong Lu, Tingzeng Wu. 2025-12-22. The number of rooted spanning forests of bicirculant graphs. https://arxiv.org/abs/2512.19256

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