{"?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-08BLNX3M/e24d9833-464e-405f-83a1-04d2bb8cab87/PDF","dcterms:extent":"330 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-08BLNX3M/0f4e12ac-56e6-43f2-bdf3-2915d2f0bcf6/TEXT","dcterms:extent":"22 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-08BLNX3M","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Deng, Hanyuan","Huang, Guihua","Kuang, Meijun"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 197-207"}],"dc:identifier":["COBISSID:17589081","ISSN:1855-3966","URN:URN:NBN:SI:doc-08BLNX3M"],"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 value"},{"@xml:lang":"en","#text":"expected value"},{"@xml:lang":"en","#text":"Kirchhoff index"},{"@xml:lang":"sl","#text":"Kirchhoffov indeks"},{"@xml:lang":"sl","#text":"matematično upanje (pričakovana vrednost)"},{"@xml:lang":"sl","#text":"polifenilna veriga"},{"@xml:lang":"en","#text":"polyphenyl chain"},{"@xml:lang":"sl","#text":"povprečna vrednost"},{"@xml:lang":"en","#text":"resistance distance"},{"@xml:lang":"sl","#text":"rezistenčna razdalja"},{"@xml:lang":"en","#text":"spiro chain"},{"@xml:lang":"sl","#text":"spiro veriga"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The expected values of Kirchhoff indices in the random polyphenyl and spiro chains|"},"dc:description":[{"@xml:lang":"sl","#text":"The Kirchhoff index ?$Kf(G)$? of a graph ?$G$? is the sum of resistance distances between all pairs of vertices in ?$G$?. In this paper, we obtain exact formulas for the expected values of the Kirchhoff indices of the random polyphenyl and spiro chains, which are graphs of a class of unbranched multispiro molecules and polycyclic aromatic hydrocarbons. Moreover, we obtain a relation between the expected values of the Kirchhoff indices of a random polyphenyl and its random hexagonal squeeze, and the average values for the Kirchhoff indices of all polyphenyl chains and all spiro chains with ?$n$? hexagons, respectively"},{"@xml:lang":"sl","#text":"Kirchoffov indeks ?$Kf(G)$? grafa ?$G$? je definiran kot vsota rezistenčnih razdalj med vsemi pari vozlišč v ?$G$?. V članku izpeljemo eksaktne formule za matematično upanje Kirchoffovih indeksov slučajnih polifenilov in spiro verig, t.j. grafov razreda nerazvejanih multispiro molekul in policikličnih aromatičnih ogljikovodikov. Najdemo tudi zvezo med pričakovanimi vrednostmi Kirchhoffovih indeksov slučajnega polifenila in njegovega slučajnega šestkotniškega ekstrakta, pa tudi med povprečnimi vrednostmi Kirchhoffovih indeksov vseh polifenilnih verig in vseh spiro verig z ?$n$? šestkotniki"}],"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-08BLNX3M","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-08BLNX3M"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-08BLNX3M/e24d9833-464e-405f-83a1-04d2bb8cab87/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-08BLNX3M/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-08BLNX3M"}}}}