{"?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-CUPHKKGK/f2d3425e-57a5-4ba7-aab9-f48c75bba080/PDF","dcterms:extent":"313 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-CUPHKKGK/5c8e6822-b256-49c5-8cec-7a1bc89d69c4/TEXT","dcterms:extent":"31 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-CUPHKKGK","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Knor, Martin","Komorník, Jozef","Škrekovski, Riste","Tepeh, Aleksandra"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 455-466"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18803801","URN:URN:NBN:SI:doc-CUPHKKGK"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"enociklični grafi"},{"@xml:lang":"en","#text":"girth"},{"@xml:lang":"sl","#text":"Graovac-Pisanski indeks"},{"@xml:lang":"en","#text":"Graovac-Pisanski index"},{"@xml:lang":"sl","#text":"modificirani Wienerjev indeks"},{"@xml:lang":"en","#text":"modified Wiener index"},{"@xml:lang":"en","#text":"unicyclic graphs"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Unicyclic graphs with the maximal value of Graovac-Pisanski index|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G$? be a graph and let ?$\\Gamma$? be its group of automorphisms. Graovac-Pisanski index of ?$G$? is ?$GP(G) = \\frac{|V(G)|}{2|\\Gamma|} \\sum_{u \\in V(G)} \\sum_{\\alpha \\in \\Gamma} d(u, \\alpha(u))$?, where ?$d(u, v)$? is the distance from ?$u$? to ?$v$? in ?$G$?. One can observe that ?$GP(G) = 0$? if ?$G$? has no nontrivial automorphisms, but it is not known which graphs attain the maximum value of Graovac-Pisanski index. In this paper we show that among unicyclic graphs on ?$n$? vertices the ?$n$?-cycle attains the maximum value of Graovac-Pisanski index"},{"@xml:lang":"sl","#text":"Naj bo ?$G$? graf in ?$\\Gamma$? njegova grupa avtomorfizmov. Graovac-Pisanski indeks grafa ?$G$? je ?$GP(G) = \\frac{|V(G)|}{2|\\Gamma|} \\sum_{u \\in V(G)} \\sum_{\\alpha \\in \\Gamma} d(u, \\alpha(u))$?, kjer je ?$d(u, v)$? razdalja med vozliščema ?$u$? in ?$v$? grafa ?$G$?. Opazimo lahko, da je ?$GP(G) = 0$?, če ?$G$? nima netrivialnih avtomorfizmov, ni pa znano, kateri grafi dosežejo maksimalno vrednost Graovac-Pisanski indeksa. V članku pokažemo, da so med enocikličnimi grafi na ?$n$? vozliščih ?$n$?-cikli tisti, ki dosežejo maksimalno vrednost Graovac-Pisanski indeksa"}],"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-CUPHKKGK","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-CUPHKKGK"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-CUPHKKGK/f2d3425e-57a5-4ba7-aab9-f48c75bba080/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-CUPHKKGK/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-CUPHKKGK"}}}}