{"?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-C6965GLZ/7fb845e1-2572-489d-b18c-9429b3caccca/PDF","dcterms:extent":"392 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-C6965GLZ/eae2cd85-7b30-436c-8d12-b7b3703ba24f/TEXT","dcterms:extent":"38 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-C6965GLZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2026","dc:creator":["Bašić, Nino","Damnjanović, Ivan","Fowler, Patrick W."],"dc:format":[{"@xml:lang":"sl","#text":"letnik:"},{"@xml:lang":"sl","#text":"številka:, article"},{"@xml:lang":"sl","#text":"str. 1-15"}],"dc:identifier":["DOI:10.26493/1855-3974.3641.49c","ISSN:1855-3966","COBISSID_HOST:264594691","URN:URN:NBN:SI:doc-C6965GLZ"],"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":"circulant graph"},{"@xml:lang":"sl","#text":"cirkulantni graf"},{"@xml:lang":"en","#text":"graph spectra"},{"@xml:lang":"sl","#text":"ničelnost"},{"@xml:lang":"en","#text":"nullity"},{"@xml:lang":"en","#text":"nut graph"},{"@xml:lang":"sl","#text":"orešni graf"},{"@xml:lang":"en","#text":"regular graph"},{"@xml:lang":"sl","#text":"regularni graf"},{"@xml:lang":"sl","#text":"spekter grafa"}],"dcterms:temporal":{"@rdf:resource":"2008-2026"},"dc:title":{"@xml:lang":"sl","#text":"On the degrees of regular nut graphs and Cayley nut graphs|"},"dc:description":{"@xml:lang":"sl","#text":"A nut graph is a simple graph for which the adjacency matrix has a single zero eigenvalue such that all non-zero kernel eigenvectors have no zero entry. It is known that infinitely many $d$-regular nut graphs exist for $3 \\leq d \\leq 12$ and for $d \\geq 4$ such that $d \\equiv 0 \\pmod{4}$. Here it is shown that infinitely many $d$-regular nut graphs exist for each degree $d \\geq 3$. Likewise, it is known that infinitely many $d$-regular Cayley nut graphs exist for $d \\geq 4$ such that $d \\equiv 0 \\pmod{4}$. Here we prove that there are infinitely many $d$-regular Cayley nut graphs for each even $d \\ge 4$. This implies that we have identified all feasible degrees $d$ for which a $d$-regular Cayley nut graph exists"},"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-C6965GLZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-C6965GLZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-C6965GLZ/7fb845e1-2572-489d-b18c-9429b3caccca/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-C6965GLZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-C6965GLZ"}}}}