Automorphism groups of Cayley graphs generated by general transposition sets
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929230300839936 |
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| author | Gijswijt, Dion de Meijer, Frank |
| author_facet | Gijswijt, Dion de Meijer, Frank |
| contents | In this paper we study the Cayley graph $\mathrm{Cay}(S_n,T)$ of the symmetric group $S_n$ generated by a set of transpositions $T$. We show that for $n\geq 5$ the Cayley graph is normal. As a corollary, we show that its automorphism group is a direct product of $S_n$ and the automorphism group of the transposition graph associated to $T$. This provides an affirmative answer to a conjecture raised by Ganesan in arXiv:1703.08109, showing that $\mathrm{Cay}(S_n,T)$ is normal if and only if the transposition graph is not $C_4$ or $K_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_17860 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphism groups of Cayley graphs generated by general transposition sets Gijswijt, Dion de Meijer, Frank Combinatorics Discrete Mathematics In this paper we study the Cayley graph $\mathrm{Cay}(S_n,T)$ of the symmetric group $S_n$ generated by a set of transpositions $T$. We show that for $n\geq 5$ the Cayley graph is normal. As a corollary, we show that its automorphism group is a direct product of $S_n$ and the automorphism group of the transposition graph associated to $T$. This provides an affirmative answer to a conjecture raised by Ganesan in arXiv:1703.08109, showing that $\mathrm{Cay}(S_n,T)$ is normal if and only if the transposition graph is not $C_4$ or $K_n$. |
| title | Automorphism groups of Cayley graphs generated by general transposition sets |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2401.17860 |