{"?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-3MO9Y4EV/41ba47e5-0902-407f-aa2d-4efa4cab8583/PDF","dcterms:extent":"1740 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-3MO9Y4EV/19d2b34e-41a7-4360-8609-7026a89a4acf/TEXT","dcterms:extent":"29 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-3MO9Y4EV/0be9ebf6-efc5-4eb4-b8fc-02843b89a77a/PDF","dcterms:extent":"111 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-3MO9Y4EV/b647f5ff-8457-431c-a29c-c12e59bab443/TEXT","dcterms:extent":"3 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-3MO9Y4EV","dcterms:issued":"2025","dc:creator":["Graver, Jack E.","Hartung, Elizabeth J."],"dc:format":[{"@xml:lang":"sl","#text":"letnik:1"},{"@xml:lang":"sl","#text":"številka:1, article   p1.05"},{"@xml:lang":"sl","#text":"str. 1-11"}],"dc:identifier":["DOI:10.26493/2820-6657.7.9ae","ISSN:2820-6657","COBISSID_HOST:285430787","URN:URN:NBN:SI:doc-3MO9Y4EV"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"University of Primorska"},"dc:source":{"@xml:lang":"sl","#text":"Discrete mathematical chemistry"},"dc:subject":[{"@xml:lang":"en","#text":"chemical graph theory"},{"@xml:lang":"en","#text":"Clar number"},{"@xml:lang":"sl","#text":"Clarovo število"},{"@xml:lang":"en","#text":"Fries number"},{"@xml:lang":"sl","#text":"Friesovo število"},{"@xml:lang":"sl","#text":"fulereni"},{"@xml:lang":"en","#text":"fullerenes"},{"@xml:lang":"en","#text":"Kekulé structure"},{"@xml:lang":"sl","#text":"Kekuléjeva struktura"},{"@xml:lang":"sl","#text":"kemijska teorija grafov"},{"@xml:lang":"en","#text":"leapfrog fullerenes"},{"@xml:lang":"en","#text":"perfect matching"},{"@xml:lang":"sl","#text":"popolno prirejanje"},{"@xml:lang":"sl","#text":"preskakovalni fulereni"}],"dc:title":{"@xml:lang":"sl","#text":"Clar numbers of leapfrog fullerenes|"},"dc:description":[{"@xml:lang":"sl","#text":"A fullerene is a 3-regular plane graph with only hexagonal and pentagonal faces. The Fries number of a fullerene G, F(G), is the maximum number of benzene rings over all possible Kekulé structures for G. The Clar number of G, C(G), is the maximum number of independent benzene rings possible over all possible Kekulé structures for G. In this paper, we show that for leapfrog fullerenes, any set of faces attaining the Clar number is a subset of faces attaining the Fries number. This property is false for fullerenes in general (as shown in paper from E. J. Hartung in 2014). We then show that if L(G) is the leapfrog of a fullerene G, then the Clar number of L(G) is equal to the vertex independence number of G"},{"@xml:lang":"sl","#text":"Fuleren je 3-regularen planarni graf, ki ima le šestkotna in petkotna lica. Friesovo število fulerena G,F(G), je največje število benzenovih obročev v vseh možnih Kekuléjevih strukturah za G. Clarovo število G, C (G), je največje število neodvisnih benzenovih obročev v vseh možnih Kekuléjevih strukturah za G. V tem članku pokažemo, da je za preskakovalne fulerene vsaka množica lic, ki doseže Clarovo število, podmnožica množice lic, ki doseže Friesovo število. Ta lastnost ne velja za fulerene v splošnem. Nato pokažemo, da če je L (G) preskakovalni fuleren od G, potem je Clarovo število L (G) enako vozliščnemu neodvisnostnemu številu grafa G"}],"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-3MO9Y4EV","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-3MO9Y4EV"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-3MO9Y4EV/41ba47e5-0902-407f-aa2d-4efa4cab8583/PDF"},"edm:rights":{"@rdf:resource":"http://creativecommons.org/licenses/by-sa/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"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-3MO9Y4EV/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-3MO9Y4EV"}}}}