{"?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-RB0X46ZH/21581e74-cf37-427f-8c2f-1b126de6b8b4/PDF","dcterms:extent":"414 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-RB0X46ZH/554c1b3f-8b83-4bc3-8404-26bfe9dc47e0/TEXT","dcterms:extent":"56 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-RB0X46ZH","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":["Potočnik, Primož","Vidali, Janoš"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 349-368"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18803545","URN:URN:NBN:SI:doc-RB0X46ZH"],"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":"cubic"},{"@xml:lang":"en","#text":"girth"},{"@xml:lang":"en","#text":"girth-regular"},{"@xml:lang":"sl","#text":"graf"},{"@xml:lang":"en","#text":"graph"},{"@xml:lang":"sl","#text":"kubični grafi"},{"@xml:lang":"sl","#text":"ožina"},{"@xml:lang":"sl","#text":"ožinska regularnost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Girth-regular graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"We introduce a notion of a girth-regular graph as a ?$k$?-regular graph for which there exists a non-descending sequence ?$(a_1, a_2, \\dots , a_k)$? (called the signature) giving, for every vertex ?$u$? of the graph, the number of girth cycles the edges with end-vertex ?$u$? lie on. Girth-regularity generalises two very different aspects of symmetry in graph theory: that of vertex transitivity and that of distance-regularity. For general girth-regular graphs, we give some results on the extremal cases of signatures. We then focus on the cubic case and provide a characterisation of cubic girth-regular graphs of girth up to 5"},{"@xml:lang":"sl","#text":"Ožinsko regularne grafe definiramo kot ?$k$?-regularne grafe, za katere obstaja nepadajo če zaporedje ?$(a_1, a_2, \\dots , a_k)$? (imenovano podpis), ki za vsako vozlišče ?$u$? v grafu pove, v koliko ožinskih ciklih (tj. ciklih najmanjše dolžine) ležijo povezave s krajiščem v vozlišču ?$u$?. Ožinska regularnost posplošuje dva zelo različna vidika simetrije v teoriji grafov: vozliščno tranzitivnost in razdaljno regularnost. Za splošne ožinsko regularne grafe podamo nekaj rezultatov o ekstremalnih primerih podpisa. Nato se osredotočimo na kubične ožinsko regularne grafe, za katere podamo karakterizacijo v primeru, ko je ožina največ 5"}],"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-RB0X46ZH","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-RB0X46ZH"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-RB0X46ZH/21581e74-cf37-427f-8c2f-1b126de6b8b4/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-RB0X46ZH/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-RB0X46ZH"}}}}