{"?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-QQZRSKJJ/f306be61-0843-4bc4-bafc-e4582ccf972a/PDF","dcterms:extent":"528 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-QQZRSKJJ/a19d9eeb-fba1-4f7c-bca8-62014e2a924a/TEXT","dcterms:extent":"76 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-QQZRSKJJ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Zhang, Mi-Mi","Zhou, Jin-Xin"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 175-200"}],"dc:identifier":["DOI:10.26493/1855-3974.2373.c02","COBISSID_HOST:112328963","ISSN:1855-3966","URN:URN:NBN:SI:doc-QQZRSKJJ"],"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":"bi-Cayley"},{"@xml:lang":"sl","#text":"bi-Cayleyjev"},{"@xml:lang":"sl","#text":"bi-diedrski graf"},{"@xml:lang":"en","#text":"bi-dihedrant"},{"@xml:lang":"en","#text":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"sl","#text":"diedrska grupa"},{"@xml:lang":"sl","#text":"diedrski graf"},{"@xml:lang":"en","#text":"dihedral group"},{"@xml:lang":"en","#text":"dihedrant"},{"@xml:lang":"sl","#text":"ne-Cayleyjev"},{"@xml:lang":"en","#text":"non-Cayley"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Trivalent dihedrants and bi-dihedrants|"},"dc:description":[{"@xml:lang":"sl","#text":"A Cayley (resp. bi-Cayley) graph on a dihedral group is called a dihedrant (resp. bi-dihedrant). In 2000, a classification of trivalent arc-transitive dihedrants was given by D. Marušič and T. Pisanski \"Symmetries of hexagonal molecular graphs on the torus\", Croat. Chem. Acta 73, No. 4, 969-981 (2000), https://hrcak.srce.hr/131972 and several years later, trivalent non-arc-transitive dihedrants of order ?$4p$? or ?$8p$? (?$p$? a prime) were classified by Feng et al. As a generalization of these results, our first result presents a classification of trivalent non-arc-transitive dihedrants. Using this, a complete classification of trivalent vertex-transitive non-Cayley bi-dihedrants is given, thus completing the study of trivalent bi-dihedrants initiated in our previous paper Discrete Math. 340, No. 8, 1757-1772 (2017). As a by-product, we generalize a theorem in The Electron. J. Comb. 19, No. 1, Research Paper P53, 13 p. (2012)"},{"@xml:lang":"sl","#text":"Cayleyjev (oz. bi-Cayleyjev) graf diedrske grupe se imenuje diedrski (oz. bi-diedrski graf). Leta 2000 sta Marušič in Pisanski predstavila klasifikacijo trivalentnih ločno-tranzitivnih diedrskih grafov, nekaj let kasneje pa so Feng in dr. klasificirali tiste trivalentne diedrske grafe reda ?$4p$? ali ?$8p$? (kjer je ?$p$? praštevilo), ki niso ločno tranzitivni. V tem članku posplošiva te rezultate; najprej predstaviva klasifikacijo tistih trivalentnih diedrskih grafov, ki niso ločno tranzitivni. Na tej osnovi podava popolno klasifikacijo trivalentnih točkovno tranzitivnih ne-Cayleyjevih bi-diedrskih grafov, s čimer zaključiva raziskavo trivalentnih bi-diedrskih grafov, ki sva jo začela v najinem prejšnjem članku Discrete Math. 340 (2017) 1757-1772. Poleg tega posplošiva še izrek iz The Electron. J. Comb. 19, No. 1, Research Paper P53, 13 p. (2012)"}],"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-QQZRSKJJ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-QQZRSKJJ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-QQZRSKJJ/f306be61-0843-4bc4-bafc-e4582ccf972a/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-QQZRSKJJ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-QQZRSKJJ"}}}}