On Isomorphisms of Tetravalent Cayley Digraphs over Dihedral Groups
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911958216736768 |
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| author | Xie, Jin-Hua Lu, Zai Ping Feng, Yan-Quan |
| author_facet | Xie, Jin-Hua Lu, Zai Ping Feng, Yan-Quan |
| contents | Let $m$ be a positive integer. A group $G$ is said to be an $m$-DCI-group or an $m$-CI-group if $G$ has the $k$-DCI property or $k$-CI property for all positive integers $k$ at most $m$, respectively. Let $G$ be a dihedral group of order $2n$ with $n\geq 3$. Qu and Yu proved that $G$ is an $m$-DCI-group or $m$-CI-group, for every $m\in \{1,2,3\}$, if and only if $n$ is odd. In this paper, it is shown that $G$ is a $4$-DCI-group if and only if $n$ is odd and not divisible by $9$, and $G$ is a $4$-CI-group if and only if $n$ is odd. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Isomorphisms of Tetravalent Cayley Digraphs over Dihedral Groups Xie, Jin-Hua Lu, Zai Ping Feng, Yan-Quan Combinatorics 05C25, 20B25 Let $m$ be a positive integer. A group $G$ is said to be an $m$-DCI-group or an $m$-CI-group if $G$ has the $k$-DCI property or $k$-CI property for all positive integers $k$ at most $m$, respectively. Let $G$ be a dihedral group of order $2n$ with $n\geq 3$. Qu and Yu proved that $G$ is an $m$-DCI-group or $m$-CI-group, for every $m\in \{1,2,3\}$, if and only if $n$ is odd. In this paper, it is shown that $G$ is a $4$-DCI-group if and only if $n$ is odd and not divisible by $9$, and $G$ is a $4$-CI-group if and only if $n$ is odd. |
| title | On Isomorphisms of Tetravalent Cayley Digraphs over Dihedral Groups |
| topic | Combinatorics 05C25, 20B25 |
| url | https://arxiv.org/abs/2407.12457 |