{"?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-IVL5ZOT2/de52e21a-6970-4fcc-9564-427974e2e04d/PDF","dcterms:extent":"301 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-IVL5ZOT2/9be1541f-c642-4550-9f30-c695fd2e0ce7/TEXT","dcterms:extent":"28 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-IVL5ZOT2","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":["Gorzkowska, Aleksandra","Kalinowski, Rafał","Pilśniak, Monika"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:12"},{"@xml:lang":"sl","#text":"str. 77-87"}],"dc:identifier":["COBISSID:18094937","ISSN:1855-3966","URN:URN:NBN:SI:doc-IVL5ZOT2"],"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":"grafi"},{"@xml:lang":"sl","#text":"kartezični produkt grafov"},{"@xml:lang":"sl","#text":"razlikovalni indeks"},{"@xml:lang":"sl","#text":"uničenje simetrij"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The distinguishing index of the Cartesian product of finite graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"The distinguishing index ?$D'(G)$? of a graph ?$G$? is the least natural number ?$d$? such that ?$G$? has an edge colouring with ?$d$? colours that is only preserved by the identity automorphism. In this paper we investigate the distinguishing index of the Cartesian product of connected finite graphs. We prove that for every ?$k \\ge 2$?, the ?$k$?-th Cartesian power of a connected graph ?$G$? has distinguishing index equal 2, with the only exception ?$D'(K_2^2) = 3$?. We also prove that if ?$G$? and ?$H$? are connected graphs that satisfy the relation ?$2 \\le |G| \\le |H| \\le 2^{|G|}(2^{|G|} - 1) - |G| + 2$?, then ?$D'(G \\Box H) \\le 2$? unless ?$G \\Box H = K_2^2$?"},{"@xml:lang":"sl","#text":"Razlikovalni indeks ?$D'(G)$? grafa ?$G$? je najmanjše naravno število ?$d$?, pri katerem ima ?$G$? barvanje povezav z ?$d$? barvami, ki ga ohranja samo identični avtomorfizem. V tem članku obravnavamo razlikovalni indeks kartezičnega produkta povezanih končnih grafov. Dokažemo, da ima ?$k$?-ta kartezična potenca povezanega grafa ?$G$? razlikovalni indeks enak 2 za vsak ?$k \\ge 2$?, z edino izjemo ?$D'(K_2^2) = 3$?. Dokažemo tudi, da, če sta ?$G$? in ?$H$? povezana grafa, ki zadoščata relaciji ?$2 \\le |G| \\le |H| \\le 2^{|G|}(2^{|G|} - 1) - |G| + 2$?, potem je ?$D'(G \\Box H) \\le 2$? razen ?$G \\Box H = K_2^2$?"}],"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-IVL5ZOT2","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-IVL5ZOT2"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-IVL5ZOT2/de52e21a-6970-4fcc-9564-427974e2e04d/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-IVL5ZOT2/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-IVL5ZOT2"}}}}