{"?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-ENFNC271/eca12ccd-7d9a-4cce-a22f-4e96b0c6dd6e/PDF","dcterms:extent":"374 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-ENFNC271/63e2c2ac-2b30-442e-84ef-dce6df1126c3/TEXT","dcterms:extent":"45 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-ENFNC271","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":"Pilśniak, Monika","dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 259-274"}],"dc:identifier":["COBISSID:18354777","ISSN:1855-3966","URN:URN:NBN:SI:doc-ENFNC271"],"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":"barvanje povezav"},{"@xml:lang":"sl","#text":"graf brez trizobov"},{"@xml:lang":"sl","#text":"ravninski graf"},{"@xml:lang":"sl","#text":"razlikovalni indeks"},{"@xml:lang":"sl","#text":"zlom simetrije v grafu"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Improving upper bounds for the distinguishing index|"},"dc:description":[{"@xml:lang":"sl","#text":"The distinguishing index of a graph ?$G$?, denoted by ?$D^\\prime(G)$?, is the least number of colours in an edge colouring of ?$G$? not preserved by any non-trivial automorphism. We characterize all connected graphs ?$G$? with ?$D^\\prime(G)\\geq \\Delta(G)$?. We show that ?$D^\\prime(G)\\leq 2$? if ?$G$? is a traceable graph of order at least seven, and ?$D^\\prime(G)\\leq 3$? if ?$G$? is either claw-free or 3-connected and planar. We also investigate the Nordhaus-Gaddum type relation: ?$2\\leq D^\\prime(G)+D^\\prime(\\overline{G})\\leq \\max\\{\\Delta(G),\\Delta(\\overline{G})\\}+2$? and we confirm it for some classes of graphs"},{"@xml:lang":"sl","#text":"Razlikovalni indeks grafa ?$G$?, označen z ?$D^\\prime(G)$?, je najmanjše število barv v barvanju povezav grafa ?$G$?, ki ga ne ohranja noben netrivialni avtomorfizem. Karakteriziramo vse povezane grafe ?$G$?, ki ustrezajo pogoju ?$D^\\prime(G)\\geq \\Delta(G)$?. Pokažemo da je ?$D^\\prime(G)\\leq 2$?, če je ?$G$? sledljiv graf reda najmanj sedem, in da je ?$D^\\prime(G)\\leq 3$? če je ?$G$? bodisi brez trizobov ali pa je 3-povezan in planaren. Raziskujemo tudi relacijo tipa Nordhaus-Gaddum: ?$2\\leq D^\\prime(G)+D^\\prime(\\overline{G})\\leq \\max\\{\\Delta(G),\\Delta(\\overline{G})\\}+2$? in jo potrdimo za določene razrede grafov"}],"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-ENFNC271","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-ENFNC271"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-ENFNC271/eca12ccd-7d9a-4cce-a22f-4e96b0c6dd6e/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-ENFNC271/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-ENFNC271"}}}}