{"?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-137M8L1I/dd496dac-f853-4d5b-beba-771bb5afd554/PDF","dcterms:extent":"519 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-137M8L1I/96fe547c-cd7a-4c61-9049-834b67e8a102/TEXT","dcterms:extent":"65 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-137M8L1I","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Amarra, Carmen","Giudici, Michael","Praeger, Cheryl E."],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 137-165"}],"dc:identifier":["COBISSID:18199385","ISSN:1855-3966","URN:URN:NBN:SI:doc-137M8L1I"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"Cayleyevi grafi"},{"@xml:lang":"sl","#text":"linearne grupe"},{"@xml:lang":"sl","#text":"permutacijske grupe"},{"@xml:lang":"sl","#text":"simetrični grafi"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Affine primitive symmetric graphs of diameter two|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$n$? be a positive integer, ?$q$? be a prime power, and ?$V$? be a vector space of dimension ?$n$? over ?$\\mathbb{F}_{q}$?. Let ?$G := V \\rtimes G_{0}$?, where ?$G_{0}$? is an irreducible subgroup of ?$GL(V)$? which is maximal by inclusion with respect to being intransitive on the set of nonzero vectors. We are interested in the class of all diameter two graphs ?$\\Gamma$? that admit such a group ?$G$? as an arc-transitive, vertex-quasiprimitive subgroup of automorphisms. In particular, we consider those graphs for which ?$G_{0}$? is a subgroup of either ?$\\Gamma\\mathrm{L}(n,q)$? or ?$\\Gamma \\mathrm{Sp}(n, q)$? and is maximal in one of the Aschbacher classes ?$\\mathcal{C}_{i}$?, where ?$i \\in \\{2, 4, 5, 6, 7, 8\\}$?. We are able to determine all graphs ?$\\Gamma$? which arise from ?$G_{0}\\leq \\Gamma\\mathrm{L}(n,q)$? with ?$i \\in \\{2, 4, 8\\}$?, and from ?$G_{0} \\leq \\Gamma \\mathrm{Sp}(n, q)$? with ?$i \\in \\{2, 8\\}$?. For the remaining classes we give necessary conditions in order for ?$\\Gamma$? to have diameter two, and in some special subcases determine all ?$G$?-symmetric diameter two graphs"},{"@xml:lang":"sl","#text":"Naj bo ?$n$? pozitivno celo število, ?$q$? potenca praštevila in ?$V$? vektorski prostor dimenzije ?$n$? nad ?$\\mathbb{F}_{q}$?. Naj bo ?$G := V \\rtimes G_{0}$?, kjer je ?$G_{0}$? ireducibilna podgrupa grupe ?$GL(V)$?, ki je maksimalna za relacijo inkluzije med podgrupami, intranzitivnimi na množici neničelnih vektorjev. Zanima nas razred ?$\\Gamma$? vseh grafov premera dve, ki dopuščajo takšno grupo ?$G$? kot ločno-tranzitivno, vozliščno-kvaziprimitivno podgrupo avtomorfizmov. Še posebej obravnavamo tiste grafe, za katere je ?$G_{0}$? podgrupa bodisi ?$\\Gamma \\mathrm{L}(n,q)$? ali ?$\\Gamma \\mathrm{Sp}(n, q)$? in je maksimalna v enem od Aschbacherjevih razredov ?$\\mathcal{C}_{i}$?, kjer je ?$i \\in \\{2, 4, 5, 6, 7, 8\\}$?. Uspelo nam je določiti vse grafe ?$\\Gamma$? ki nastanejo iz ?$G_{0}\\leq \\Gamma \\mathrm{L}(n,q)$?, kjer je ?$i \\in \\{2, 4, 8\\}$?, in ?$G_{0} \\leq \\Gamma \\mathrm{Sp}(n, q)$? kjer je ?$i \\in \\{2, 8\\}$?. Za preostale razrede navedemo potrebne pogoje za to, da ima ?$\\Gamma$? premer dve, in v nekaj posebnih podprimerih določimo vse ?$G$?-simetrične grafe premera dve"}],"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-137M8L1I","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-137M8L1I"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-137M8L1I/dd496dac-f853-4d5b-beba-771bb5afd554/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-137M8L1I/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-137M8L1I"}}}}