{"paper":{"title":"Arc-transitive pentavalent Cayley graphs with soluble vertex stabilizer on finite nonabelian simple groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ben Gong Lou, Bo Ling","submitted_at":"2017-02-19T14:24:05Z","abstract_excerpt":"A Cayley graph $\\Ga=\\Cay(G,S)$ is said to be normal if $G$ is normal in $\\Aut\\Ga$. The concept of normal Cayley graphs was first proposed by M.Y.Xu in [Discrete Math. 182, 309-319, 1998] and it plays an important role in determining the full automorphism groups of Cayley graphs. In this paper, we investigate the normality problem of the connected arc-transitive pentavalent Cayley graphs with soluble vertex stabilizer on finite nonabelian simple groups. We prove that all such graphs $\\Ga$ are either normal or $G=\\A_{39}$ or $\\A_{79}$. Further, a connected arc-transitive pentavalent Cayley graph"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.05754","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"}