{"?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-JXMAARTZ/5634cd58-f703-4e66-8658-7c5de92b400e/PDF","dcterms:extent":"1015 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JXMAARTZ/40e3fbba-122a-4797-8b28-93cfb6133486/TEXT","dcterms:extent":"46 KB"}],"edm:TimeSpan":{"@rdf:about":"2008-2026","edm:begin":{"@xml:lang":"en","#text":"2008"},"edm:end":{"@xml:lang":"en","#text":"2026"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-JXMAARTZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-FNN1A9OB"},{"@xml:lang":"sl","#text":"Obzornik za matematiko in fiziko"}],"dcterms:issued":"2025","dc:creator":"Jurišić, Aleksandar","dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:letn 72"},{"@xml:lang":"sl","#text":"str. 41-62"}],"dc:identifier":["ISSN:0473-7466","COBISSID_HOST:248772355","URN:URN:NBN:SI:doc-JXMAARTZ"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"sl","#text":"četverokotniki"},{"@xml:lang":"en","#text":"finite geometries"},{"@xml:lang":"sl","#text":"grafi"},{"@xml:lang":"en","#text":"graphs"},{"@xml:lang":"sl","#text":"končne geometrije"},{"@xml:lang":"sl","#text":"matematika"},{"@xml:lang":"en","#text":"mathematics"},{"@xml:lang":"en","#text":"quadrilaterals"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"Svet brez trikotnikov|"},"dc:description":[{"@xml:lang":"sl","#text":"A brief introduction to generalized quadrilaterals is presented (some simple properties and constructions). In simple terms these are finite geometries with no triangles (in contrast to projective planes). They are also a special case of partial geometries, and of generalized ?$n$?-gons. The collinearity graphs of partial geometries are strongly regular, which leads to properties of graph eigenvalues and also to Moore graphs (i.e., graphs in which the girth equals twice the diameter plus one, such as the pentagon and the Petersen graph). Finally, some open problems and exercises are presented guiding the reader from the basics to modern questions at the intersection of finite geometries and graphs"},{"@xml:lang":"sl","#text":"Podamo kratek uvod v posplošene četverokotnike (nekaj enostavnih lastnosti in konstrukcij). Poenostavljeno gre za končne geometrije brez trikotnikov (v nasprotju s projektivnimi ravninami). So tudi poseben primer delnih geometrij, pa tudi posplošenih ?$n$?-kotnikov. Grafi kolinearnosti delnih geometrij so krepko regularni, kar vodi do lastnosti lastnih vrednosti grafov, pa tudi Moorovih grafov (tj. grafov, pri katerih velja, da je ožina enaka dvakratniku premera, povečanega za ?$1$?, npr. petkotnik ter Petersenov graf). Na koncu so izpostavljeni nekateri odprti problemi in naloge, ki vodijo bralca od osnov do sodobnih vprašanj na presečišču končnih geometrij in grafov"}],"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-JXMAARTZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-JXMAARTZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-JXMAARTZ/5634cd58-f703-4e66-8658-7c5de92b400e/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by-sa/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":"Društvo matematikov, fizikov in astronomov"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-JXMAARTZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-JXMAARTZ"}}}}