{"?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-Y6YMRBT1/5d827d2b-d109-4ee2-aa0c-a9a824a06358/HTML","dcterms:extent":"34 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-Y6YMRBT1/5eca3ab8-4135-4022-907b-7a534a7b3e8c/PDF","dcterms:extent":"991 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-Y6YMRBT1/089534e7-1f87-4e75-a925-5111e395b094/TEXT","dcterms:extent":"24 KB"}],"edm:TimeSpan":{"@rdf:about":"1998-2025","edm:begin":{"@xml:lang":"en","#text":"1998"},"edm:end":{"@xml:lang":"en","#text":"2025"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-Y6YMRBT1","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-KC6O72BG"},{"@xml:lang":"sl","#text":"Acta chimica slovenica"}],"dcterms:issued":"2005","dc:creator":["Vukičević, Damir","Žerovnik, Janez"],"dc:format":[{"@xml:lang":"sl","#text":"10 strani"},{"@xml:lang":"sl","#text":"številka:3"},{"@xml:lang":"sl","#text":"letnik:52"},{"@xml:lang":"sl","#text":"str. 272-281"}],"dc:identifier":["ISSN:1318-0207","COBISSID:9929238","URN:URN:NBN:SI:doc-Y6YMRBT1"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Slovensko kemijsko društvo"},"dc:subject":[{"@xml:lang":"en","#text":"chemistry"},{"@xml:lang":"sl","#text":"kemija"},{"@xml:lang":"sl","#text":"matematika"},{"@xml:lang":"en","#text":"mathematics"},{"@xml:lang":"sl","#text":"teorija grafov"},{"@xml:lang":"sl","#text":"topološki indeksi"},{"@xml:lang":"sl","#text":"Wienerjev indeks"}],"dcterms:temporal":{"@rdf:resource":"1998-2025"},"dc:title":{"@xml:lang":"sl","#text":"Altered Wiener indices|"},"dc:description":{"@xml:lang":"sl","#text":"Recently Nikolić, Trinajstič and Randić put forward a novel modification ?$^mW(G)$? of the Wiener index ?$W(G)$?, defined as ?$^mW(G) = \\sum_{u,v \\in E(G)} n_G(u,v)^{-1} n_G(v,u)^{-1}$?. This definition was generalized to $^mW(G) = \\sum_{u,v \\in E(G)} n_G(u,v)^{\\lambda} n_G(v,u)^{\\lamba}$ by Gutman and the present authors. Another class of modified indices ?$_{\\lambda$}W(G) = \\frac{1}{2} \\sum_{uv \\in E(G)} (v(G)^\\lammda - n_G(u,v)^\\lambda - n_G(v,u)^\\lambda)$? is studied here. It is shown that some of main properties of ?$W(G)$?, $^mW(G)$ and $^{\\lambda}W(G)$ are also properties of $_{\\lambda}W(G)$, valid for all values of the parameter ?$\\lambda \\ne 0$?. In particular, if ?$T_n$? is any ?$n$?-vertex tree, different from the ?$n$?-vertex path ?$P_n$? and the ?$n$?-vertex star ?$S_n$?, then for any ?$\\lambda > 1$?, ?$_\\lambda W(P_n) > _\\lambda W(T_n) > \\lambda W(S_n)$?, vhereas for any ?$\\lambda <1$?, $_\\lambda W(P_n) < _\\lambda W(T_n) < \\lambda W(S_n)$. Thus ?$_\\lambda W(G)$? provides a novel class of structure-descriptors, suitable for modeling branching-dependent properties of organic compounds, applicable in QSPR and QSAR studies. We also demonstrate that if trees are ordered with regard to ?$_\\lambda W(G)$? then, in the general case, this ordering is different for different ?$\\lambda$?"},"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-Y6YMRBT1","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-Y6YMRBT1"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-Y6YMRBT1/5eca3ab8-4135-4022-907b-7a534a7b3e8c/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":"Slovensko kemijsko društvo"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-Y6YMRBT1/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-Y6YMRBT1"}}}}