Integral Cayley graphs over a group of order $6n$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914641782767616 |
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| author | Wang, Jing Liu, Xiaogang Wang, Ligong |
| author_facet | Wang, Jing Liu, Xiaogang Wang, Ligong |
| contents | In this paper, we study the integral Cayley graphs over a non-abelian group $U_{6n}=\langle a,b\mid a^{2n}=b^3=1, a^{-1}ba=b^{-1}\rangle$ of order $6n$. We give a necessary and sufficient condition for the integrality of Cayley graphs over $U_{6n}$. We also study relationships between the integrality of Cayley graphs over $U_{6n}$ and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over $U_{6n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_07069 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integral Cayley graphs over a group of order $6n$ Wang, Jing Liu, Xiaogang Wang, Ligong Combinatorics 05C50, 05C25 In this paper, we study the integral Cayley graphs over a non-abelian group $U_{6n}=\langle a,b\mid a^{2n}=b^3=1, a^{-1}ba=b^{-1}\rangle$ of order $6n$. We give a necessary and sufficient condition for the integrality of Cayley graphs over $U_{6n}$. We also study relationships between the integrality of Cayley graphs over $U_{6n}$ and the Boolean algebra of cyclic groups. As applications, we construct some infinite families of connected integral Cayley graphs over $U_{6n}$. |
| title | Integral Cayley graphs over a group of order $6n$ |
| topic | Combinatorics 05C50, 05C25 |
| url | https://arxiv.org/abs/2401.07069 |