Enumeration of dicirculant digraphs
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917770795417600 |
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| author | Wang, Jing Wang, Ligong Liu, Xiaogang |
| author_facet | Wang, Jing Wang, Ligong Liu, Xiaogang |
| contents | Let $T_{4p}=\langle a,b\mid a^{2p}=1,a^p=b^2, b^{-1}ab=a^{-1}\rangle$ be the dicyclic group of order $4p$. A Cayley digraph over $T_{4p}$ is called a dicirculant digraph. In this paper, we calculate the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) up to isomorphism by using the Pólya Enumeration Theorem. Moreover, we get the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) and out-degree $k$ for every $k$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_04695 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Enumeration of dicirculant digraphs Wang, Jing Wang, Ligong Liu, Xiaogang Combinatorics Let $T_{4p}=\langle a,b\mid a^{2p}=1,a^p=b^2, b^{-1}ab=a^{-1}\rangle$ be the dicyclic group of order $4p$. A Cayley digraph over $T_{4p}$ is called a dicirculant digraph. In this paper, we calculate the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) up to isomorphism by using the Pólya Enumeration Theorem. Moreover, we get the number of (connected) dicirculant digraphs of order $4p$ ($p$ prime) and out-degree $k$ for every $k$. |
| title | Enumeration of dicirculant digraphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.04695 |