{"?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-E7LFDSTN/3a8cdd93-10dc-42f3-8867-f5fa7b1aa5db/PDF","dcterms:extent":"383 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-E7LFDSTN/a4eea47f-7ebc-43bc-9349-8511bb004f83/TEXT","dcterms:extent":"58 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-E7LFDSTN","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":["Dam, Edwin Robert van","Jazaeri, Mojtaba"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 203-222"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18954073","URN:URN:NBN:SI:doc-E7LFDSTN"],"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":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"en","#text":"distance-regular graph"},{"@xml:lang":"sl","#text":"razdaljno-regularen graf"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Distance-regular Cayley graphs with small valency|"},"dc:description":[{"@xml:lang":"sl","#text":"We consider the problem of which distance-regular graphs with small valency are Cayley graphs. We determine the distance-regular Cayley graphs with valency at most 4, the Cayley graphs among the distance-regular graphs with known putative intersection arrays for valency 5, and the Cayley graphs among all distance-regular graphs with girth 3 and valency 6 or 7. We obtain that the incidence graphs of Desarguesian affine planes minus a parallel class of lines are Cayley graphs. We show that the incidence graphs of the known generalized hexagons are not Cayley graphs, and neither are some other distance-regular graphs that come from small generalized quadrangles or hexagons. Among some ''exceptional'' distance-regular graphs with small valency, we find that the Armanios-Wells graph and the Klein graph are Cayley graphs"},{"@xml:lang":"sl","#text":"Problem, ki ga obravnavamo, sprašuje, kateri razdaljno-regularni grafi z majhno valenco so Cayleyjevi grafi. Poišcemo Cayleyjeve grafe med razdaljno-regularnimi grafi z valenco kvecjemu 4, med razdaljno-regularnimi grafi za znane domnevne presečne tabele z valenco 5 in med vsemi razdaljno-regularnimi grafi z ožino 3 in valenco 6 ali 7. Ugotovimo, da so incidenčni grafi Desarguesovih afinih ravnin brez enega razreda vzporednih premic Cayleyjevi grafi. Pokažemo, da incidenčni grafi znanih posplošenih šestkotnikov niso Cayleyjevi grafi; prav tako niso Cayleyjevi nekateri drugi razdaljno-regularni grafi, ki izhajajo iz majhnih posplošenih štirikotnikov ali šestkotnikov. Med ''izjemnimi'' razdaljno-regularnimi grafi z majhno valenco smo našli dva, ki sta Cayleyjeva, in sicer sta to Armanios-Wellsov graf in Kleinov graf"}],"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-E7LFDSTN","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-E7LFDSTN"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-E7LFDSTN/3a8cdd93-10dc-42f3-8867-f5fa7b1aa5db/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-E7LFDSTN/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-E7LFDSTN"}}}}