{"?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-DK81OO1P/43ba516b-9e56-4b4c-bf1f-dfb000a4fd76/PDF","dcterms:extent":"269 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DK81OO1P/312162d2-245b-40e3-85cd-1e172c40233b/TEXT","dcterms:extent":"21 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-DK81OO1P","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":["Broere, Izak","Pilśniak, Monika"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"str. 15-21"}],"dc:identifier":["COBISSID:18173273","ISSN:1855-3966","URN:URN:NBN:SI:doc-DK81OO1P"],"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":"avtomorfizem"},{"@xml:lang":"sl","#text":"barvanje povezav"},{"@xml:lang":"sl","#text":"neskončni graf"},{"@xml:lang":"sl","#text":"neskončnodimenzionalna hiperkocka"},{"@xml:lang":"sl","#text":"razlikovalni indeks"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The distinguishing index of the Cartesian product of countable graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"The distinguishing index ?$D'(G)$? of a graph ?$G$? is the least cardinal ?$d$? such that ?$G$? has an edge colouring with ?$d$? colours that is preserved only by the trivial automorphism. We derive some bounds for this parameter for infinite graphs. In particular, we investigate the distinguishing index of the Cartesian product of countable graphs. Finally, we prove that ?$D'(K^{\\aleph_0}_2) = 2$?, where ?$K^{\\aleph_0}_2$? is the infinite dimensional hypercube"},{"@xml:lang":"sl","#text":"Razlikovalni indeks ?$D'(G)$? grafa ?$G$? je najmanjše kardinalno število ?$d$?, pri katerem ima graf ?$G$? barvanje povezav z ?$d$? barvami, ki ga ohranja samo trivialni avtomorfizem. Izpeljemo nekaj mej za ta parameter pri neskončnih grafih. Še posebej raziskujemo razlikovalni indeks kartezičnega produkta števnih grafov. Nazadnje dokažemo, da velja ?$D'(K^{\\aleph_0}_2) = 2$?, kjer je ?$K^{\\aleph_0}_2$? neskončnodimenzionalna hiperkocka"}],"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-DK81OO1P","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-DK81OO1P"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-DK81OO1P/43ba516b-9e56-4b4c-bf1f-dfb000a4fd76/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-DK81OO1P/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-DK81OO1P"}}}}