{"paper":{"title":"Automorphism groups of a class of cubic Cayley graphs on symmetric groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lu Lu, Qiongxiang Huang, Xueyi Huang","submitted_at":"2016-09-17T15:01:45Z","abstract_excerpt":"Let $S_n$ denote the symmetric group of degree $n$ with $n\\geq 3$. Set $S=\\{c_n=(1\\ 2\\ldots \\ n),c_n^{-1},(1\\ 2)\\}$. Let $\\Gamma_n=\\mathrm{Cay}(S_n,S)$ be the Cayley graph on $S_n$ with respect to $S$. In this paper, we show that $\\Gamma_n$ ($n\\geq 13$) is a normal Cayley graph, and that the full automorphism group of $\\Gamma_n$ is equal to $\\mathrm{Aut}(\\Gamma_n)=R(S_n)\\rtimes \\langle\\mathrm{Inn}(\\phi)\\rangle\\cong S_n\\rtimes \\mathbb{Z}_2$, where $R(S_n)$ is the right regular representation of $S_n$, $\\phi=(1\\ 2)(3\\ n)(4\\ n-1)(5\\ n-2)\\cdots$ $(\\in S_n)$, and $\\mathrm{Inn}(\\phi)$ is the inner i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.05348","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}