{"?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-UJ744LW5/b5b82118-9d30-4c2c-8c85-18caa5d29c48/PDF","dcterms:extent":"345 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UJ744LW5/ef8c85d4-f882-4ebc-9ff8-3fb4674fe146/TEXT","dcterms:extent":"24 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-UJ744LW5","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":"Pilśniak, Monika","dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:20"},{"@xml:lang":"sl","#text":"str. 223-231"}],"dc:identifier":["DOI:10.26493/1855-3974.2173.71a","ISSN:1855-3966","COBISSID_HOST:92014595","URN:URN:NBN:SI:doc-UJ744LW5"],"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"},{"@xml:lang":"sl","#text":"meje Nordhaus-Gaddumovega tipa"},{"@xml:lang":"en","#text":"Nordhaus-Gaddum type bounds"},{"@xml:lang":"sl","#text":"razlikovalni indeks"},{"@xml:lang":"en","#text":"symmetry breaking in graphs"},{"@xml:lang":"sl","#text":"zlom simetrije v grafih"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Nordhaus-Gaddum type inequalities for the distinguishing index|"},"dc:description":[{"@xml:lang":"sl","#text":"The distinguishing index of a graph ?$G$?, denoted by ?$D'(G)$?, is the least number of colours in an edge colouring of ?$G$? not preserved by any nontrivial automorphism. This invariant is defined for any graph without ?$K_2$? as a connected component and without two isolated vertices, and such a graph is called admissible. We prove the Nordhaus-Gaddum type relation: ?$$2 \\le D'(G) + D'(\\overline{G}) \\le \\Delta (G)+2$$? for every admissible connected graph ?$G$? of order ?$|G|\\ge 7$? such that ?$\\overline{G}$? is also admissible"},{"@xml:lang":"sl","#text":"Razlikovalni indeks grafa ?$G$?, označen z ?$D'(G)$?, je najmanjše število barv v barvanju povezav grafa ?$G$?, tako da tega barvanja ne ohranja noben netrivialen avtomorfizem grafa ?$G$?. Ta invarianta je definirana za vsak graf, ki ne vsebuje grafa ?$K_2$? kot povezane komponente, pa tudi ne dveh izoliranih vozlišč; takšnemu grafu pravimo dopusten graf. Dokažemo, da velja naslednja neenakost Nordhaus-Gaddumovega tipa: ?$$2 \\le D'(G) + D'(\\overline{G}) \\le \\Delta (G)+2$$? za vsak dopusten povezan graf ?$G$? reda ?$|G|\\ge 7$?, ki izpolnjuje dodaten pogoj, da je tudi ?$\\overline{G}$? dopusten graf"}],"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-UJ744LW5","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-UJ744LW5"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-UJ744LW5/b5b82118-9d30-4c2c-8c85-18caa5d29c48/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-UJ744LW5/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-UJ744LW5"}}}}