Enumeration of Cayley graphs over a nonabelian group of order $8p$
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912551367868416 |
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| author | Ye, Bei Liu, Xiaogang Wang, Jing |
| author_facet | Ye, Bei Liu, Xiaogang Wang, Jing |
| contents | Let $T_{8p} = \left\langle a,b\mid a^{2p}=b^8=e,a^p=b^4,b^{-1}ab=a^{-1} \right\rangle$ be a nonabelian group of order $8p$, where $p$ is an odd prime number. In this paper, we give the formula to calculate the number of Cayley graphs over $T_{8p}$ up to isomorphism by using the Pólya Enumeration Theorem. Moreover, we get the formula to calculate the number of connected Cayley graphs over $T_{8p}$ by deleting the disconnected graphs. By applying the results, we list the exact number of (connected) Cayley graphs for $3\leq p \leq 13$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_17035 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Enumeration of Cayley graphs over a nonabelian group of order $8p$ Ye, Bei Liu, Xiaogang Wang, Jing Combinatorics Let $T_{8p} = \left\langle a,b\mid a^{2p}=b^8=e,a^p=b^4,b^{-1}ab=a^{-1} \right\rangle$ be a nonabelian group of order $8p$, where $p$ is an odd prime number. In this paper, we give the formula to calculate the number of Cayley graphs over $T_{8p}$ up to isomorphism by using the Pólya Enumeration Theorem. Moreover, we get the formula to calculate the number of connected Cayley graphs over $T_{8p}$ by deleting the disconnected graphs. By applying the results, we list the exact number of (connected) Cayley graphs for $3\leq p \leq 13$. |
| title | Enumeration of Cayley graphs over a nonabelian group of order $8p$ |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.17035 |