Edge pancyclic Cayley graphs on symmetric group
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866916905105752064 |
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| author | Cao, Mengyu Lu, Mei Lv, Zequn Zhao, Xiamiao |
| author_facet | Cao, Mengyu Lu, Mei Lv, Zequn Zhao, Xiamiao |
| contents | We study the derangement graph $Γ_n$ whose vertex set consists of all permutations of $\{1,\ldots,n\}$, where two vertices are adjacent if and only if their corresponding permutations differ at every position. It is well-known that $Γ_n$ is a Cayley graph, Hamiltonian and Hamilton-connected. In this paper, we prove that for $n \geq 4$, the derangement graph $Γ_n$ is edge pancyclic. Moreover, we extend this result to two broader classes of Cayley graphs defined on symmetric group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_12618 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Edge pancyclic Cayley graphs on symmetric group Cao, Mengyu Lu, Mei Lv, Zequn Zhao, Xiamiao Combinatorics We study the derangement graph $Γ_n$ whose vertex set consists of all permutations of $\{1,\ldots,n\}$, where two vertices are adjacent if and only if their corresponding permutations differ at every position. It is well-known that $Γ_n$ is a Cayley graph, Hamiltonian and Hamilton-connected. In this paper, we prove that for $n \geq 4$, the derangement graph $Γ_n$ is edge pancyclic. Moreover, we extend this result to two broader classes of Cayley graphs defined on symmetric group. |
| title | Edge pancyclic Cayley graphs on symmetric group |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2508.12618 |