{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-EJBGXQIN/b343494e-97d1-491c-a7f1-c2d5db72db66/PDF","dcterms:extent":"381 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-EJBGXQIN/421cc4ca-b8eb-467c-ade8-e93279de2a3d/TEXT","dcterms:extent":"38 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2025","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-EJBGXQIN","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Ling, Bo","Lou, Ben Gong","Wu, Ci Xuan"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"str. 81-95"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18702681","URN:URN:NBN:SI:doc-EJBGXQIN"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"en","#text":"arc-transitive graphs"},{"@xml:lang":"en","#text":"automorphism group"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov"},{"@xml:lang":"sl","#text":"ločno-tranzitiven graf"},{"@xml:lang":"en","#text":"normal quotient"},{"@xml:lang":"sl","#text":"normalni kvocient"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Pentavalent symmetric graphs of order four times an odd square-free integer|"},"dc:description":[{"@xml:lang":"sl","#text":"A graph is said to be symmetric if its automorphism group is transitive on its arcs. S.-T. Guo et al. Electron. J. Comb. 18, No. 1, Research Paper P233, 13 p. (2011) and J. Pan et al. Electron. J. Comb. 20, No. 1, Research Paper P36, 9 p. (2013) determined all pentavalent symmetric graphs of order ?$4pq$?. In this paper, we shall generalize this result by determining all connected pentavalent symmetric graphs of order four times an odd square-free integer. It is shown in this paper that, for each such graph ?$\\mathit{\\Gamma}$?, either the full automorphism group ?$\\mathrm{Aut}\\mathit{\\Gamma}$? is isomorphic to ?$\\mathrm{PSL}(2, p)$?, ?$\\mathrm{PGL}(2, p)$?, ?$\\mathrm{PSL}(2, p) \\times \\mathbb{Z}_2$? or ?$\\mathrm{PGL}(2, p) \\times \\mathbb{Z}_2$?, or ?$\\mathit{\\Gamma}$? is isomorphic to one of 9 graphs"},{"@xml:lang":"sl","#text":"Za graf pravimo, da je simetričen, če je njegova grupa avtomorfizmov tranzitivna na množici njegovih lokov. Guo in dr. v 2011 ter Pan in dr. v 2013 so določili vse petvalentne simetrične grafe reda ?$4pq$?. V članku posplošimo ta rezultat in določimo vse povezane petvalentne simetrične grafe, katerih red je štirikratnik lihega števila brez kvadratnih faktorjev. Pokažemo, da za vsak tak graf ?$\\mathit{\\Gamma}$? velja, da je polna grupa avtomorfizmov ?$\\mathrm{Aut}\\mathit{\\Gamma}$? izomorfna eni od grup ?$\\mathrm{PSL}(2, p)$?, ?$\\mathrm{PGL}(2, p)$?, ?$\\mathrm{PSL}(2, p) \\times \\mathbb{Z}_2$?, $?\\mathrm{PGL}(2, p) \\times \\mathbb{Z}_2$?, ali pa je graf ?$\\mathit{\\Gamma}$? izomorfen enemu od 9 grafov"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"znanstveno časopisje"},{"@xml:lang":"en","#text":"journals"},{"@rdf:resource":"http://www.wikidata.org/entity/Q361785"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:doc-EJBGXQIN","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-EJBGXQIN"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-EJBGXQIN/b343494e-97d1-491c-a7f1-c2d5db72db66/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by/4.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-EJBGXQIN/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-EJBGXQIN"}}}}