{"?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-O9PGQOKQ/b533d550-cb87-49e7-b1a2-7a0573f12e98/PDF","dcterms:extent":"481 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-O9PGQOKQ/37063789-2a55-456a-ad33-4c1b26a4ad27/TEXT","dcterms:extent":"60 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-O9PGQOKQ/3d9cf6b9-a997-4f61-8f8c-8fb12cc10345/PDF","dcterms:extent":"132 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-O9PGQOKQ/5bc69ac8-a57b-462a-b2c9-1bccd5d129e9/TEXT","dcterms:extent":"5 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-O9PGQOKQ","dcterms:issued":"2026","dc:creator":["Abdollahi, Alireza","Arezoomand, Majid","Feng, Tao","Wang, Shixin"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"številka:3, article  p3.06"},{"@xml:lang":"sl","#text":"str. 1-21"}],"dc:identifier":["DOI:10.26493/1855-3974.3351.3b6","ISSN:1855-3974","COBISSID_HOST:289903363","URN:URN:NBN:SI:doc-O9PGQOKQ"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:source":{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"},"dc:subject":[{"@xml:lang":"en","#text":"algebraic degree"},{"@xml:lang":"sl","#text":"algebrajska stopnja"},{"@xml:lang":"en","#text":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyjev graf"},{"@xml:lang":"en","#text":"characters of groups"},{"@xml:lang":"sl","#text":"grupni karakterji"},{"@xml:lang":"en","#text":"integral eigenvalue"},{"@xml:lang":"sl","#text":"integralna lastna vrednost"}],"dc:title":{"@xml:lang":"sl","#text":"On 2-integral Cayley graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper, we introduce the concept of k-integral graphs. A graph ? is called k-integral if the extension degree of the splitting field of the characteristic polynomial of ? over rational field Q is equal to k. We prove that for any positive integers k and ?, the set of all finite connected graphs with algebraic degree at most k and maximum degree at most ? is finite. We study 2-integral Cayley graphs over finite groups G with respect to Cayley sets which are a union of conjugacy classes of G. Among other general results, we completely characterize all finite abelian groups having a connected 2-integral Cayley graph with valency 2, 3, 4 and 5. Furthermore, we classify the finite groups G that al Cayley graphs over G with bounded valency are 2-integral"},{"@xml:lang":"sl","#text":"V tem članku uvedemo pojem k-integralnih grafov. Graf ? imenujemo k-integralen, če je stopnja razširitve razcepnega polja karakterističnega polinoma grafa ? nad poljem racionalnih števil Q enaka k. Dokažemo, da je množica vseh končnih povezanih grafov z dano algebrajsko stopnjo in dano največjo stopnjo vozlišč končna. Grafi, ki so 1-integralni, so natanko integralni grafi, torej grafi, katerih vse lastne vrednosti so cela števila. Preučujemo 2-integralne Cayleyjeve grafe nad končnimi grupami G glede na Cayleyjeve množice, ki so unije konjugiranostnih razredov grupe G. Med drugim popolnoma okarakteriziramo vse končne abelove grupe, ki imajo povezan 2-integralen Cayleyjev graf valence 2, 3, 4 ali 5. Nadalje klasificiramo vse končne grupe G, za katere so vsi Cayleyjevi grafi nad G z omejeno valenco 2-integralni"}],"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-O9PGQOKQ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-O9PGQOKQ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-O9PGQOKQ/b533d550-cb87-49e7-b1a2-7a0573f12e98/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-O9PGQOKQ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-O9PGQOKQ"}}}}