{"?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-Q8SKBRM4/c1486d32-06b1-4f18-9a1a-e15b8f81a8df/PDF","dcterms:extent":"402 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-Q8SKBRM4/32799f08-57bc-4d47-8efd-6cbca483d504/TEXT","dcterms:extent":"38 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-Q8SKBRM4","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":["Abrams, Lowell","Lauderdale, Lindsey-Kay"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 243-257"}],"dc:identifier":["DOI:10.26493/1855-3974.2351.07b","COBISSID_HOST:112665603","ISSN:1855-3966","URN:URN:NBN:SI:doc-Q8SKBRM4"],"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":"chemical graph theory"},{"@xml:lang":"en","#text":"distance number"},{"@xml:lang":"en","#text":"Graovac-Pisanski index"},{"@xml:lang":"en","#text":"graph automorphism group"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov grafa"},{"@xml:lang":"sl","#text":"indeks Graovac-Pisanskega"},{"@xml:lang":"sl","#text":"kemijska teorija grafov"},{"@xml:lang":"sl","#text":"razdaljno število"},{"@xml:lang":"en","#text":"Wiener index"},{"@xml:lang":"sl","#text":"Wienerjev indeks"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Density results for Graovac-Pisanski’s distance number|"},"dc:description":[{"@xml:lang":"sl","#text":"The sum of distances between every pair of vertices in a graph ?$G$? is called the Wiener index of ?$G$?. This graph invariant was initially utilized to predict certain physico-chemical properties of organic compounds. However, the Wiener index of ?$G$? does not account for any of its symmetries, which are also known to effect these physico-chemical properties. A. Graovac and I. Pisanski On the Wiener index of a graph, J. Math. Chem. 8, No. 1, 53-62 (1991; doi:10.1007/BF01166923) modified the Wiener index of ?$G$? to measure the average distance each vertex is displaced under the elements of the symmetry group of ?$G$?; we call this the Graovac-Pisanski (GP) distance number of ?$G$?. In this article, we prove that the set of all GP distance numbers of graphs with isomorphic symmetry groups is dense in a half-line. Moreover, for each finite group ?$\\Gamma$? and each rational number ?$q$? within this half-line, we present a construction for a graph whose GP distance number is ?$q$? and whose symmetry group is isomorphic to ?$\\Gamma$?. This construction results in graphs whose vertex orbits are not connected; we also consider an analogous construction which ensures that all vertex orbits are connected"},{"@xml:lang":"sl","#text":"Vsota razdalj med vsemi pari točk v grafu ?$G$? se imenuje Wienerjev indeks grafa ?$G$?. Ta grafovska invarianta se je najprej uporabljala za napovedovanje določenih fizikalnokemijskih lastnosti organskih spojin. VendarWienerjev indeks grafa ?$G$? ne upošteva nobene od njegovih simetrij, za katere pa je prav tako znano, da vplivajo na te fizikalno-kemijske lastnosti. Graovac in Pisanski sta modificirala Wienerjev indeks grafa ?$G$? tako, da meri povprečno razdaljo, za katero je vsaka točka prestavljena, če nanjo delujejo elementi grupe simetrij grafa ?$G$?; tako spremenjenemu indeksu pravimo razdaljno število Graovac-Pisanskega za graf ?$G$?. V tem dokažemo, da je množica vseh razdaljnih števil Graovac-Pisanskega za grafe z izomorfnimi simetrijskimi grupami gosta na določenem poltraku. Poleg tega, za vsako končno grupo ?$\\Gamma$? in vsako racionalno število ?$q$? s tega poltraka predstavimo konstrukcijo grafa, katerega razdaljno število Graovac-Pisanskega je ?$q$? in katerega simetrijska grupa je izomorfna ?$\\Gamma$?. Ta konstrukcija nam da grafe, katerih točkovne orbite niso povezane; obravnavamo pa tudi analogno konstrukcijo, ki zagotavlja, da so vse točkovne orbite povezane"}],"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-Q8SKBRM4","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-Q8SKBRM4"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-Q8SKBRM4/c1486d32-06b1-4f18-9a1a-e15b8f81a8df/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-Q8SKBRM4/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-Q8SKBRM4"}}}}