{"?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-0BBBH5HP/e8462b76-1b99-45e2-b496-13d7b35024dc/PDF","dcterms:extent":"490 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-0BBBH5HP/e6cf270e-4da7-4416-a6df-4ac85a78b3ee/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-0BBBH5HP","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Minchenko, Marsha","Wanless, Ian M."],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 381-408"}],"dc:identifier":["COBISSID:17377881","ISSN:1855-3966","URN:URN:NBN:SI:doc-0BBBH5HP"],"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":"arc-transitive"},{"@xml:lang":"en","#text":"Cayley graph"},{"@xml:lang":"sl","#text":"Cayleyev graf"},{"@xml:lang":"sl","#text":"celoštevilski graf"},{"@xml:lang":"en","#text":"graph homomorphism"},{"@xml:lang":"en","#text":"graph spectrum"},{"@xml:lang":"sl","#text":"homomorfizem grafov"},{"@xml:lang":"en","#text":"integral graph"},{"@xml:lang":"sl","#text":"ločno-tranzitiven"},{"@xml:lang":"sl","#text":"prirejanje napetosti"},{"@xml:lang":"sl","#text":"spekter grafa"},{"@xml:lang":"en","#text":"vertex-transitive bipartite double cover"},{"@xml:lang":"en","#text":"voltage assignment"},{"@xml:lang":"sl","#text":"vozliščno tranzitiven dvodelen dvojni krov"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Quartic integral Cayley graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"We give exhaustive lists of connected 4-regular integral Cayley graphs and connected 4-regular integral arc-transitive graphs. An integral graph is a graph for which all eigenvalues are integers. A Cayley graph ?$\\text{Cay}(\\Gamma, S)$? for a given group ?$\\Gamma$? and connection set ?$S \\subset \\Gamma$? is the graph with vertex set ?$\\Gamma$? and with ?$a$? connected to ?$b$? if and only if ?$ba^{-1} \\in S$?. Up to isomorphism, we find that there are 32 connected quartic integral Cayley graphs; 17 of which are bipartite. Many of these can be realized in a number of different ways by using non-isomorphic choices for ?$\\Gamma$? and/or different choices for ?$S$?. A graph is arc-transitive if its automorphism group acts transitively upon ordered pairs of adjacent vertices. Up to isomorphism, there are 27 quartic integral graphs that are arc-transitive. Of these 27 graphs, 16 are bipartite and 16 are Cayley graphs. By taking quotients of our Cayley or arc-transitive graphs we also find a number of other quartic integral graphs. Overall, we find 9 new spectra that can be realised by bipartite quartic integral graphs"},{"@xml:lang":"sl","#text":"Navajamo popolna seznama povezanih križnih, t.j. 4-regularnih celoštevilskih Cayleyevih grafov in povezanih 4-regularnih celoštevilskih ločno-tranzitivnih grafov. Celoštevilski graf je graf s samimi celoštevilskimi lastnimi vrednostmi. Cayleyev graf ?$\\text{Cay}(\\Gamma, S)$? za dano grupo ?$\\Gamma$? in povezavno množico ?$S \\subset \\Gamma$? je graf z množico vozlišč ?$\\Gamma$?, v katerem je vozlišče ?$a$? povezano z vozliščem ?$b$? če in samo če je ?$ba^{-1} \\in S$?. Do izomorfizma natanko smo ugotovili, da je 32 povezanih 4-regularnih celoštevilskih Cayleyevih grafov; 17 od njih je dvodelnih. Mnoge od njih se da realizirati na mnogo različnih načinov z uporabo ne-izomorfnih izbir za ?$\\Gamma$? in/ali ?$S$?. Graf se imenuje ločno-tranzitiven, če njegova grupa avtomorfizmov deluje tranzitivno na urejenih parih sosednjih vozlišč. Do izomorfizma natanko obstaja 27 4-regularnih celoštevilskih ločno tranzitivnih grafov. Med temi 27 grafi je 16 dvodelnih in 16 Cayleyevih. Tudi številni drugi 4-regularni celoštevilski grafi so kvocienti naših Cayleyevih ali ločno-tranzitivnih grafov. V splošnem smo našli 9 novih spektrov, ki jih lahko realiziramo z dvodelnimi 4-regularnimi celoštevilskimi grafi"}],"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-0BBBH5HP","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-0BBBH5HP"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-0BBBH5HP/e8462b76-1b99-45e2-b496-13d7b35024dc/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-0BBBH5HP/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-0BBBH5HP"}}}}