{"?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-9MRS2ONV/a0f55a2b-e125-4ee5-b35b-2c75d83fa496/PDF","dcterms:extent":"453 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-9MRS2ONV/187ef839-b181-4cb7-8830-2c134cf502af/TEXT","dcterms:extent":"56 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-9MRS2ONV","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2017","dc:creator":["Borg, Martha","Fowler, Patrick W.","Pickup, Barry T.","Sciriha, Irene"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 379-408"}],"dc:identifier":["COBISSID:18365273","ISSN:1855-3966","URN:URN:NBN:SI:doc-9MRS2ONV"],"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":"karakteristični polinom"},{"@xml:lang":"sl","#text":"lastne vrednosti"},{"@xml:lang":"sl","#text":"matrika sosednosti"},{"@xml:lang":"sl","#text":"molekulska prevodnost"},{"@xml:lang":"sl","#text":"uteženi grafi"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Spectra and structural polynomials of graphs of relevance to the theory of molecular conduction|"},"dc:description":[{"@xml:lang":"sl","#text":"In chemistry and physics, distortivity of ?$\\pi$?-systems (stabilisation of bond-alternated structures) is an important factor in the calculation of geometric, energetic, and electronic properties of molecules via graph theoretical methods. We use the spectra of paths and cycles with alternating vertex and edge weights to obtain the eigenvalues and eigenvectors for a class of linear and cyclic ladders with alternating rung and backbone edge weights. We derive characteristic polynomials and other structural polynomials formed from the cofactors of the characteristic matrix for these graphs. We also obtain spectra and structural polynomials for ladders with flipped weights and/or Möbius topology. In all cases, the structural polynomials for the composite graphs are expressed in terms of products of polynomials for graphs of half order. This form of the expressions allows global deductions about the transmission spectra of molecular devices in the graph-theoretical theory of ballistic molecular conduction"},{"@xml:lang":"sl","#text":"V kemiji in fiziki je distortivnost ?$\\pi$?-sistemov (stabilizacija vezi-alternirajocih struktur) pomembna pri računanju geometrijskih, energijskih in elektronskih lastnosti molekul s pomočjo metod teorije grafov. Uporabimo spektre poti in ciklov z alternirajočimi vozliščnimi in po vezavnimi utežmi, da dobimo lastne vrednosti in lastne vektorje za razred linearnih in cikličnih lestev z alternirajocimi povezavnimi utežmi. Izpeljemo karakteristične polinome in druge strukturne polinome, dobljene iz kofaktorjev karakteristične matrike za te grafe. Dobimo tudi spektre in strukturne polinome za lestve s preobrnjenimi utežmi in/ali Möbiusovo topologijo. V vseh primerih lahko strukturne polinome sestavljenih grafov izrazimo kot produkte polinomov grafov polovičnega reda. Ta oblika izrazov omogoča globalne izpeljave v zvezi s transmisijskimi spektri molekulskih naprav v okviru s teorijo grafov podprte teorije balistične molekulske prevodnosti"}],"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-9MRS2ONV","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-9MRS2ONV"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-9MRS2ONV/a0f55a2b-e125-4ee5-b35b-2c75d83fa496/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-9MRS2ONV/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-9MRS2ONV"}}}}