The number of rooted spanning forests of bicirculant graphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908727751213056 |
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| author | Yang, Jing Feng, Lihua Lu, Rongrong Wu, Tingzeng |
| author_facet | Yang, Jing Feng, Lihua Lu, Rongrong Wu, Tingzeng |
| contents | A bi-Cayley graph over the cyclic group $(\mathbb{Z}_n, +)$ is called a bicirculant graph. Let $Γ=BC(\mathbb{Z}_n; R,T,S)$ be a bicirculant graph with $R=-R\subseteq \mathbb{Z}_n\setminus \{0\}$ 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 $Γ$. Moreover, we investigate some arithmetic properties of the number of rooted spanning forests of $Γ$, and find its asymptotic behaviour as $n$ tends infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19256 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The number of rooted spanning forests of bicirculant graphs Yang, Jing Feng, Lihua Lu, Rongrong Wu, Tingzeng Combinatorics Algebraic Geometry 05C30 G.2.2 A bi-Cayley graph over the cyclic group $(\mathbb{Z}_n, +)$ is called a bicirculant graph. Let $Γ=BC(\mathbb{Z}_n; R,T,S)$ be a bicirculant graph with $R=-R\subseteq \mathbb{Z}_n\setminus \{0\}$ 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 $Γ$. Moreover, we investigate some arithmetic properties of the number of rooted spanning forests of $Γ$, and find its asymptotic behaviour as $n$ tends infinity. |
| title | The number of rooted spanning forests of bicirculant graphs |
| topic | Combinatorics Algebraic Geometry 05C30 G.2.2 |
| url | https://arxiv.org/abs/2512.19256 |