{"?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-O5XMSQF0/daecf422-8713-4514-98ee-29da59493176/PDF","dcterms:extent":"319 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-O5XMSQF0/907e7031-d5b5-40cf-ba9f-8a2e88d20a00/TEXT","dcterms:extent":"23 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-O5XMSQF0","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Imrich, Wilfried","Kalinowski, Rafał","Pilśniak, Monika","Woźniak, Mariusz"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:18"},{"@xml:lang":"sl","#text":"str. 117-126"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:39629315","URN:URN:NBN:SI:doc-O5XMSQF0"],"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":"distinguishing index of a graph"},{"@xml:lang":"sl","#text":"razlikovalni indeks grafa"},{"@xml:lang":"en","#text":"symmetry breaking"},{"@xml:lang":"sl","#text":"zlom simetrije"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The distinguishing index of connected graphs without pendant edges|"},"dc:description":[{"@xml:lang":"sl","#text":"We consider edge colourings, not necessarily proper. The distinguishing index ?$D'(G)$? of a graph ?$G$? is the least number of colours in an edge colouring that is preserved only by the identity automorphism. It is known that ?$D'(G) \\le \\Delta$? for every countable, connected graph ?$G$? with finite maximum degree ?$\\Delta$? except for three small cycles. We prove that ?$D'(G) \\le \\lceil\\sqrt{\\Delta}\\rceil+1$? if additionally ?$G$? does not have pendant edges"},{"@xml:lang":"sl","#text":"Obravnavamo barvanja povezav, ne nujno pravilna. Razlikovalni indeks ?$D'(G)$? grafa ?$G$? je najmanjše število barv v barvanju povezav, ki ga ohranja samo identični avtomorfizem. Znano je, da je ?$D'(G) \\le \\Delta$? za vsak števen, povezan graf ?$G$? s končno maksimalno stopnjo ?$\\Delta$? razen za tri majhne cikle. Dokažemo, da je ?$D'(G) \\le \\lceil\\sqrt{\\Delta}\\rceil+1$? ob dodatnem pogoju, da graf ?$G$? nima visečih povezav"}],"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-O5XMSQF0","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-O5XMSQF0"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-O5XMSQF0/daecf422-8713-4514-98ee-29da59493176/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-O5XMSQF0/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-O5XMSQF0"}}}}