{"?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-42YOT5WG/1c17e2e4-9a56-4f72-8beb-658c1777b3a7/PDF","dcterms:extent":"302 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-42YOT5WG/90a41a81-88b5-4d95-bb5b-eae4c4c3c246/TEXT","dcterms:extent":"40 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-42YOT5WG","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Bachratý, Martin","Širan, Jozef"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 55-67"}],"dc:identifier":["COBISSID:17368409","ISSN:1855-3966","URN:URN:NBN:SI:doc-42YOT5WG"],"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":"automorphism group"},{"@xml:lang":"en","#text":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"en","#text":"degree"},{"@xml:lang":"en","#text":"diameter"},{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov"},{"@xml:lang":"en","#text":"polarity graph"},{"@xml:lang":"sl","#text":"polarnostni graf"},{"@xml:lang":"sl","#text":"premer"},{"@xml:lang":"sl","#text":"stopnja"},{"@xml:lang":"en","#text":"vertex-transitive graph"},{"@xml:lang":"sl","#text":"vozliščno-tranzitiven graf"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Polarity graphs revisited|"},"dc:description":[{"@xml:lang":"sl","#text":"Polarity graphs, also known as Brown graphs, and their minor modifications are the largest currently known graphs of diameter 2 and a given maximum degree ?$d$? such that ?$d - 1$? is a prime power larger than 5. In view of the recent interest in the degree-diameter problem restricted to vertex-transitive and Cayley graphs we investigate ways of turning the (non-regular) polarity graphs to large vertex-transitive graphs of diameter 2 and given degree. We review certain properties of polarity graphs, giving new and shorter proofs. Then we show that polarity graphs of maximum even degree ?$d$? cannot be spanning subgraphs of vertex-transitive graphs of degree at most ?$d + 2$?. If ?$d - 1$? is a power of 2, there are two large vertex-transitive induced subgraphs of the corresponding polarity graph, one of degree ?$d - 1$? and the other of degree ?$d - 2$?. We show that the subgraphs of degree ?$d - 1$? cannot be extended to vertex-transitive graphs of diameter 2 by adding a relatively small non-edge orbital. On the positive side, we prove that the subgraphs of degree ?$d - 2$? can be extended to the largest currently known Cayley graphs of given degree and diameter 2 found by Šiagiová and the second author J. Combin. Theory Ser. B 102 (2012), 470-473"},{"@xml:lang":"sl","#text":"Polarnostni grafi, znani tudi kot Brownovi grafi, in njihove manjše modifikacije, so največji trenutno znani grafi premera 2 in dane maksimalne stopnje ?$d$?, kjer je ?$d - 1$? potenca praštevila večja od 5. V luči nedavnega zanimanja za \"problem stopenj in premera\", omejenega na vozliščno-tranzitivne in Cayleyeve grafe, raziskujemo načine, na katere bi spremenili (ne-regularne) polarnostne grafe v velike vozliščno-tranzitivne grafe premera 2 in dane stopnje. Najprej pregledamo določene lastnosti polarnostnih grafov in predstavimo nove in krajše dokaze. Nato pokažemo, da polarnostni grafi maksimalne sode stopnje ?$d$? ne morejo biti vpeti podgrafi vozliščno-tranzitivnih grafov stopnje največ ?$d + 2$?. Če je ?$d - 1$? potenca števila 2, potem obstajata dva velika vozliščno-tranzitivna inducirana podgrafa ustreznega polarnostnega grafa, eden je stopnje ?$d - 1$?, drugi pa stopnje ?$d - 2$?. Pokažemo, da podgrafov stopnje ?$d - 1$? ni mogoče razširiti do vozliščno-tranzitivnih grafov premera 2 z dodajanjem relativno majhne ne-povezavne orbitale. Dokažemo pa, da je podgrafe stopnje ?d - 2? mogoče razširiti do največjih trenutno znanih Cayleyevih grafov dane stopnje in premera 2, ki sta jih našla Šiagiová in drugi avtor J. Combin. Theory Ser. B 102 (2012), 470-473"}],"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-42YOT5WG","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-42YOT5WG"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-42YOT5WG/1c17e2e4-9a56-4f72-8beb-658c1777b3a7/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-42YOT5WG/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-42YOT5WG"}}}}