{"?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-44IRC9KA/2B3B5B4D-FB96-413E-8135-02D12E812744/PDF","dcterms:extent":"0 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-44IRC9KA/482b98c1-87d4-42ae-810a-e8ab9e3335a9/PDF","dcterms:extent":"282 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-44IRC9KA/dbc7050d-9987-49c5-9b03-d5a19dbc6e19/TEXT","dcterms:extent":"18 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-44IRC9KA","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2013","dc:creator":["Knor, Martin","Potočnik, Primož","Škrekovski, Riste"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:6"},{"@xml:lang":"sl","#text":"str. 211-219"}],"dc:identifier":["COBISSID:16472921","ISSN:1855-3966","URN:URN:NBN:SI:doc-44IRC9KA"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"claw"},{"@xml:lang":"sl","#text":"drevo"},{"@xml:lang":"en","#text":"graph theory"},{"@xml:lang":"en","#text":"line graph"},{"@xml:lang":"sl","#text":"povezavni graf"},{"@xml:lang":"sl","#text":"teorija grafov"},{"@xml:lang":"en","#text":"tree"},{"@xml:lang":"en","#text":"Wiener index"},{"@xml:lang":"sl","#text":"Wienerjev indeks"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Wiener index of iterated line graphs of trees homeomorphic to the claw K sub {1,3}|"},"dc:description":{"@xml:lang":"sl","#text":"Let ?$G$? be a graph. Denote by ?$L^i(G)$? its ?$i$?-iterated line graph and denote by ?$W(G)$? its Wiener index. Dobrynin, Entringer and Gutman stated the following problem: Does there exist a non-trivial tree ?$T$? and ?$i \\ge 3$? such that ?$W(L^i(T)) = W(T)$?? In a series of five papers we solve this problem. In a previous paper we proved that ?$W(L^i(T)) > W(T)$? for every tree ?$T$? that is not homeomorphic to a path, claw ?$K_{1,3}$? and to the graph of \"letter ?$H$?\", where ?$i \\ge 3$?. Here we prove that ?$W(L^i(T)) > W(T)$? for every tree ?$T$? homeomorphic to the claw, ?$T \\ne K_{1,3}$? and ?$i \\ge 4$?"},"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-44IRC9KA","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-44IRC9KA"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-44IRC9KA/2B3B5B4D-FB96-413E-8135-02D12E812744/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-44IRC9KA/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-44IRC9KA"}}}}