{"?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-QXPSMPH4/28eb7906-694d-4807-9c29-09deec681040/PDF","dcterms:extent":"403 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-QXPSMPH4/83467752-1684-425f-ac5a-9e4187e5f451/TEXT","dcterms:extent":"29 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-QXPSMPH4","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2016","dc:creator":["Tratnik, Niko","Žigert Pleteršek, Petra"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:11"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 425-435"}],"dc:identifier":["ISSN:1855-3966","COBISSID:22678536","URN:URN:NBN:SI:doc-QXPSMPH4"],"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":"cube polynomial"},{"@xml:lang":"en","#text":"distributive lattice"},{"@xml:lang":"sl","#text":"distributivna mreža"},{"@xml:lang":"sl","#text":"fuleren"},{"@xml:lang":"en","#text":"fullerene"},{"@xml:lang":"en","#text":"Kekulé structure"},{"@xml:lang":"sl","#text":"kekuléjska struktura"},{"@xml:lang":"sl","#text":"kockovni polinom"},{"@xml:lang":"en","#text":"median graph"},{"@xml:lang":"sl","#text":"medianski graf"},{"@xml:lang":"en","#text":"perfect matching"},{"@xml:lang":"sl","#text":"popolno prirejanje"},{"@xml:lang":"en","#text":"resonance graph"},{"@xml:lang":"sl","#text":"resonančni graf"},{"@xml:lang":"en","#text":"Zhang-Zhang polynomial"},{"@xml:lang":"sl","#text":"Zhang-Zhangov polinom"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Resonance graphs of fullerenes|"},"dc:description":[{"@xml:lang":"sl","#text":"A fullerene ?$G$? is a 3-regular plane graph consisting only of pentagonal and hexagonal faces. The resonance graph ?$R(G)$? of ?$G$? reflects the structure of its perfect matchings. The Zhang-Zhang polynomial of a fullerene is a counting polynomial of resonant structures called Clar covers. The cube polynomial is a counting polynomial of induced hypercubes in a graph. In the present paper we show that the resonance graph of every fullerene is bipartite and each connected component has girth 4 or is a path. Also, the equivalence of the Zhang-Zhang polynomial of a fullerene and the cube polynomial of its resonance graph is established. Furthermore, it is shown that every subgraph of the resonance graph isomorphic to a hypercube is an induced subgraph in the resonance graph. For benzenoid systems and tubulenes each connected component of the resonance graph is the covering graph of a distributive lattice; for fullerenes this is not true, as we show with an example"},{"@xml:lang":"sl","#text":"Fuleren ?$G$? je 3-regularen ravninski graf, sestavljen samo iz petkotniških in šestkotniških lic. Resonančni graf ?$R(G)$? grafa ?$G$? odraža strukturo njegovih popolnih prirejanj. Zhang-Zhangov polinom fulerena je preštevalni polinom (rodovna funkcija) resonančnih struktur, imenovanih Clarovi krovi. Kockovni polinom je preštevalni polinom induciranih hiperkock v grafu. V tem članku pokažemo, da je resonančni graf vsakega fulerena dvodelen in da ima vsaka njegova povezana komponenta ožino 4 ali pa je pot. Prav tako dokažemo ekvivalenco Zhang-Zhangovega polinoma fulerena in kockovnega polinoma njegovega resonanč- nega grafa. Pokažemo tudi, da je vsak podgraf resonančnega grafa izomorfen hiperkocki v induciranem podgrafu resonančnega grafa. Pri benzenoidnih sistemih in tubulenih je vsaka povezana komponenta resonančnega grafa krovni graf distributivne mreže; za fulerene to ne drži, kot pokaže primer"}],"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-QXPSMPH4","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-QXPSMPH4"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-QXPSMPH4/28eb7906-694d-4807-9c29-09deec681040/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-QXPSMPH4/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-QXPSMPH4"}}}}