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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2407.19745 |
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| _version_ | 1866914891204395008 |
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| author | Pan, Junyao |
| author_facet | Pan, Junyao |
| contents | Let $[n]^{(k)}$ be the set of all ordered $k$-tuples of distinct elements in $[n]=\{1,2,...,n\}$. The $(n,k,r)$-arrangement graph $A(n,k,r)$ with $1\leq r\leq k\leq n$, is the graph with vertex set $[n]^{(k)}$ and with two $k$-tuples are adjacent if they differ in exactly $r$ coordinates. In this manuscript, we characterize the full automorphism groups of $A(n,k,r)$ in the cases that $1\leq r=k\leq n$ and $r=2<k=n$. Thus, we resolve two special cases of an open problem proposed by Fu-Gang Yin, Yan-Quan Feng, Jin-Xin Zhou and Yu-Hong Guo. In addition, we conclude with a bold conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19745 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphism group of the graph $A(n,k,r)$ Pan, Junyao Group Theory 05C25, 05E18 Let $[n]^{(k)}$ be the set of all ordered $k$-tuples of distinct elements in $[n]=\{1,2,...,n\}$. The $(n,k,r)$-arrangement graph $A(n,k,r)$ with $1\leq r\leq k\leq n$, is the graph with vertex set $[n]^{(k)}$ and with two $k$-tuples are adjacent if they differ in exactly $r$ coordinates. In this manuscript, we characterize the full automorphism groups of $A(n,k,r)$ in the cases that $1\leq r=k\leq n$ and $r=2<k=n$. Thus, we resolve two special cases of an open problem proposed by Fu-Gang Yin, Yan-Quan Feng, Jin-Xin Zhou and Yu-Hong Guo. In addition, we conclude with a bold conjecture. |
| title | Automorphism group of the graph $A(n,k,r)$ |
| topic | Group Theory 05C25, 05E18 |
| url | https://arxiv.org/abs/2407.19745 |