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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1609.05348","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-09-17T15:01:45Z","cross_cats_sorted":[],"title_canon_sha256":"52df5dd007546012728b80c970093f2f462a480b72333503fdc46a29b95baacd","abstract_canon_sha256":"a77bf57bd5c5aa2e4e60bf7a7852a8605e0ee6d6b4c1f4d7b568380590e70f97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:04:26.657286Z","signature_b64":"MUsO3Z3WlbrnslkOGP/n/kqzCvXtrP0cxmITt0EaHyeae/Z+GTQRhNfdeI/AfZNq9pT/4G/M/sFQwH1bJDFlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4c27e9421947be9bfdd70fb3f989c24cee9c770cea105781d5dab48dd09f901","last_reissued_at":"2026-05-18T01:04:26.656441Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:04:26.656441Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $S$. 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