{"paper":{"title":"Automorphism groups of Cayley graphs generated by connected transposition sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"cs.DM","authors_text":"Ashwin Ganesan","submitted_at":"2012-05-23T15:20:17Z","abstract_excerpt":"Let $S$ be a set of transpositions that generates the symmetric group $S_n$, where $n \\ge 3$. The transposition graph $T(S)$ is defined to be the graph with vertex set $\\{1,\\ldots,n\\}$ and with vertices $i$ and $j$ being adjacent in $T(S)$ whenever $(i,j) \\in S$. We prove that if the girth of the transposition graph $T(S)$ is at least 5, then the automorphism group of the Cayley graph $\\Cay(S_n,S)$ is the semidirect product $R(S_n) \\rtimes \\Aut(S_n,S)$, where $\\Aut(S_n,S)$ is the set of automorphisms of $S_n$ that fixes $S$. This strengthens a result of Feng on transposition graphs that are tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5199","kind":"arxiv","version":4},"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"}