{"?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-712PTDUM/167ac6ac-a583-4d0a-9111-8bf3be544f07/PDF","dcterms:extent":"389 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-712PTDUM/3f8347d8-8748-424d-a346-7c48d30645ce/TEXT","dcterms:extent":"25 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-712PTDUM","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":["Graver, Jack E.","Watkins, Mark E."],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 581-589"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18965849","URN:URN:NBN:SI:doc-712PTDUM"],"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":"connectivity"},{"@xml:lang":"en","#text":"edge-transitive"},{"@xml:lang":"en","#text":"lobe"},{"@xml:lang":"en","#text":"lobe-transitive"},{"@xml:lang":"en","#text":"orbit"},{"@xml:lang":"sl","#text":"orbita"},{"@xml:lang":"sl","#text":"povezanost"},{"@xml:lang":"sl","#text":"povezavno tranzitiven"},{"@xml:lang":"sl","#text":"reženj"},{"@xml:lang":"sl","#text":"reženjsko tranzitiven"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Lobe, edge, and arc transitivity of graphs of connectivity 1|"},"dc:description":[{"@xml:lang":"sl","#text":"We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconnected graph ?$\\Lambda$? and a \"code\" assigned to each orbit of Aut?$(\\Lambda)$?, there exists a unique lobe-transitive graph ?$\\Gamma$? of connectivity 1 whose lobes are copies of ?$\\Lambda$? and is consistent with the given code at every vertex of ?$\\Gamma$?. These results lead to necessary and sufficient conditions for a graph of connectivity 1 to be edge-transitive and to be arc-transitive. Countable graphs of connectivity 1 the action of whose automorphism groups is, respectively, vertex-transitive, primitive, regular, Cayley, and Frobenius had been previously characterized in the literature"},{"@xml:lang":"sl","#text":"Podamo potrebne in zadostne pogoje za reženjsko tranzitivnost lokalno končnih in lokalno števnih grafov, katerih povezanost je enaka 1. Nadalje pokažemo, da za vsak bipovezan graf ?$\\Lambda$? in \"kodo\", prirejeno vsaki orbiti grupe Aut(?$\\Lambda$?), obstaja en sam reženjsko tranzitiven graf ?$\\Gamma$? s povezanostjo 1, katerega režnji so kopije grafa ?$\\Lambda$? in je konsistenten z dano kodo v vsakem vozlišču grafa ?$\\Gamma$?. Ti rezultati vodijo k potrebnim in zadostnim pogojem za to, da je graf s povezanostjo 1 povezavno tranzitiven in ločno tranzitiven. Števni grafi s povezanostjo 1, za katere je delovanje njihovih grup avtomorfizmov vozliščno tranzitivno, primitivno, regularno, Cayleyjevo ali Frobeniusovo, so bili v literaturi karakterizirani že prej"}],"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-712PTDUM","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-712PTDUM"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-712PTDUM/167ac6ac-a583-4d0a-9111-8bf3be544f07/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-712PTDUM/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-712PTDUM"}}}}