{"?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-0LSXUSP5/27d717f0-2176-4780-91e3-5b6afbabe449/PDF","dcterms:extent":"403 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-0LSXUSP5/56d70b0e-609c-4c63-a8c1-ffda76425c0e/TEXT","dcterms:extent":"44 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-0LSXUSP5","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":["Qin, Yan-Li","Zhou, Jin-Xin"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"str. 215-235"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18705497","URN:URN:NBN:SI:doc-0LSXUSP5"],"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-p-metacirculant"},{"@xml:lang":"sl","#text":"bi-p-metacirkulant"},{"@xml:lang":"en","#text":"edge-transitive"},{"@xml:lang":"en","#text":"inner-abelian p-group"},{"@xml:lang":"sl","#text":"notranje-abelska p-grupa"},{"@xml:lang":"sl","#text":"povezavno-tranzitiven"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Edge-transitive bi-p-metacirculants of valency p|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$p$? be an odd prime. A graph is called a bi-?$p$?-metacirculant on a metacyclic ?$p$?-group ?$H$? if admits a metacyclic ?$p$?-group ?$H$? of automorphisms acting semiregularly on its vertices with two orbits. A bi-?$p$?-metacirculant on a group ?$H$? is said to be abelian or non-abelian according to whether or not ?$H$? is abelian. By the results of A. Malnič et al. Discrete Math. 274, No. 1-3, 187-198 (2004) and Y. Feng et al. J. Graph Theory 52, No. 4, 341-352 (2006), we see that up to isomorphism, the Gray graph is the only cubic edge-transitive non-abelian bi-?$p$?-metacirculant on a group of order ?$p^3$?. This motivates us to consider the classification of cubic edge-transitive bi-?$p$?-metacirculants. Previously, we have proved that a cubic edge-transitive non-abelian bi-?$p$?-metacirculant exists if and only if ?$p = 3$?. In this paper, we give a classification of connected edge-transitive non-abelian bi-?$p$?-metacirculants of valency ?$p$?, and consequently, we complete the classification of connected cubic edge-transitive non-abelian bi-?$p$?-metacirculants"},{"@xml:lang":"sl","#text":"Naj bo ?$p$? liho praštevilo. Graf se imenuje bi-?$p$?-metacirkulant na metaciklični ?$p$?-grupi ?$H$?, če obstaja metaciklična ?$p$?-grupa ?$H$? avtomorfizmov, ki deluje polregularno na njegovih točkah, ki se glede na to delovanje razdelijo v dve orbiti. Bi-?$p$?-metacirkulant na grupi ?$H$? se imenuje abelski ali neabelski, v skladu s tem, ali je grupa ?$H$? abelska ali ni. Iz rezultatov Malniča in dr. iz 2004 ter Fenga in dr. iz leta 2006 sledi, da je, do izomorfizma natančno, Grayev graf edini kubični povezavno-tranzitivni neabelski bi-?$p$?-metacirkulant na grupi reda ?$p^3$?. To nas je motiviralo, da smo se lotili klasifikacije kubičnih povezavno-tranzitivnih bi-?$p$?-metacirkulantov. Že prej smo dokazali, da kubični povezavno-tranzitivni ne-abelski bi-?$p$?-metacirkulant obstaja natanko tedaj, ko je ?$p = 3$?. V članku podamo klasifikacijo povezanih povezavno-tranzitivnih ne-abelskih bi-?$p$?-metacirkulantov stopnje ?$p$?, s tem pa je tudi dokončana klasifikacija povezanih kubičnih povezavno-tranzitivnih ne-abelskih bi-?$p$?-metacirkulantov"}],"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-0LSXUSP5","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-0LSXUSP5"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-0LSXUSP5/27d717f0-2176-4780-91e3-5b6afbabe449/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-0LSXUSP5/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-0LSXUSP5"}}}}