{"corpus_id":45810518,"paper_sha":"9abe5169b52e14df5f3ea1ebc0c6403a57fad052","doi":"10.1016/j.ejc.2017.03.007","arxiv_id":"1701.01187","pmid":null,"pmcid":null,"mag_id":2575767884,"dblp_id":"journals/ejc/DuFZ17","acl_id":null,"title":"Pentavalent symmetric graphs admitting vertex-transitive non-abelian simple groups","year":2017,"publication_date":"2017-01-05","venue":"European journal of combinatorics (Print)","journal":{"name":"Eur. J. Comb.","pages":"134-145","volume":"63"},"journal_issn":null,"journal_title":null,"publication_types":["JournalArticle"],"pubmed_pub_types":null,"s2_fields_of_study":["Mathematics","Computer Science"],"reference_count":38,"citation_count":24,"influential_citation_count":3,"is_open_access":false,"arxiv_categories":["math.GR"],"arxiv_license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":null,"s2_open_access_landing_url":null,"s2_open_access_license":null,"s2_open_access_status":null,"pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"A graph \\Gamma is said to be {\\em symmetric} if its automorphism group \\Aut(\\Gamma) is transitive on the arc set of \\Gamma. Let $G$ be a finite non-abelian simple group and let \\Gamma be a connected pentavalent symmetric graph such that G\\leq \\Aut(\\Gamma). In this paper, we show that if $G$ is transitive on the vertex set of \\Gamma, then either G\\unlhd \\Aut(\\Gamma) or \\Aut(\\Gamma) contains a non-abelian simple normal subgroup $T$ such that $G\\leq T$ and $(G,T)$ is one of $58$ possible pairs of non-abelian simple groups. In particular, if $G$ is arc-transitive, then $(G,T)$ is one of $17$ possible pairs, and if $G$ is regular on the vertex set of \\Gamma, then $(G,T)$ is one of $13$ possible pairs, which improves the result on pentavalent symmetric Cayley graph given by Fang, Ma and Wang in 2011.","claims":[{"public_id":"cl_fe8d2fca5d29e15bb26c6b5bd23c525b","status":"active","text":"For a connected pentavalent symmetric graph with a vertex-transitive finite non-abelian simple subgroup of automorphisms, either that subgroup is normal in the full automorphism group or the full automorphism group has a non-abelian simple normal subgroup containing it, with the pair constrained to one of 58 possibilities.","confidence":0.98,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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