{"?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-K0YT1TOS/7718eb3b-8995-4604-882f-2e55ae3b5b3c/PDF","dcterms:extent":"372 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-K0YT1TOS/1684b733-9db7-421d-988e-37eea5fe7067/TEXT","dcterms:extent":"20 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-K0YT1TOS","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2021","dc:creator":["Chen, Yichao","Peng, Xuhui","Zhang, Jinlian"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 199-208"}],"dc:identifier":["DOI:10.26493/1855-3974.2043.fbb","ISSN:1855-3966","COBISSID_HOST:91830275","URN:URN:NBN:SI:doc-K0YT1TOS"],"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":"average genus"},{"@xml:lang":"en","#text":"bouquet of circles"},{"@xml:lang":"sl","#text":"dipol"},{"@xml:lang":"en","#text":"dipole"},{"@xml:lang":"sl","#text":"navadna diferencialna enačba"},{"@xml:lang":"en","#text":"ordinary differential equation"},{"@xml:lang":"sl","#text":"povprečni rod"},{"@xml:lang":"sl","#text":"šopek krožnic"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The average genus for bouquets of circles and dipoles|"},"dc:description":[{"@xml:lang":"sl","#text":"The bouquet of circles ?$B_n$? and dipole graph ?$D_n$? are two important classes of graphs in topological graph theory. For ?$n\\geq 1$?, we give an explicit formula for the average genus ?$\\gamma_{avg}(B_n)$? of ?$B_n$?. By this expression, one easily sees ?$\\gamma_{avg}(B_n)=\\frac{n-\\ln n-\\gamma+1-\\ln 2}{2}+o(1)$?, where ?$\\gamma$? is the Euler-Mascheroni constant. Similar results are obtained for ?$D_n$?. Our method is new and deeply depends on the knowledge in ordinary differential equations"},{"@xml:lang":"sl","#text":"Šopek krožnic ?$B_n$? in dipolni graf ?$D_n$? sta dva zelo pomembna razreda grafov v topološki teoriji grafov. Za ?$n\\geq 1$? izpeljemo eksplicitno formulo za povprečni rod ?$\\gamma_{avg}(B_n)$? grafa ?$B_n$?. Iz nje se zlahka vidi, da je ?$\\gamma_{avg}(B_n)=\\frac{n-\\ln n-\\gamma+1-\\ln 2}{2}+o(1)$?, kjer je ?$\\gamma$? Euler-Mascheronijeva konstanta. Podobne rezultate dobimo za ?$D_n$?. Naša metoda v glavnem temelji na tehniki rodovnih vrst in znanju o navadnih diferencialnih enačbah"}],"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-K0YT1TOS","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-K0YT1TOS"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-K0YT1TOS/7718eb3b-8995-4604-882f-2e55ae3b5b3c/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-K0YT1TOS/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-K0YT1TOS"}}}}