{"?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-UHT1IWT3/f7863ef4-930c-420a-ae51-b3b3412e52f7/PDF","dcterms:extent":"284 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-UHT1IWT3/25b02be8-f0cf-40ee-b2ea-5e7a2c281cbd/TEXT","dcterms:extent":"25 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-UHT1IWT3","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":["Klotz, Walter","Sander, Torsten"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:12"},{"@xml:lang":"sl","#text":"str. 155-165"}],"dc:identifier":["COBISSID:18097497","ISSN:1855-3966","URN:URN:NBN:SI:doc-UHT1IWT3"],"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 vozlišč"},{"@xml:lang":"sl","#text":"barvni razredi"},{"@xml:lang":"sl","#text":"Cayleyjevi graf"},{"@xml:lang":"sl","#text":"grafi"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Uniquely colorable Cayley graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"It is shown that the chromatic number ?$\\chi (G) = k$? of a uniquely colorable Cayley graph ?$G$? over a group ?$\\Gamma$? is a divisor of ?$|\\Gamma| = n$?. Each color class in a ?$k$?-coloring of ?$G$? is a coset of a subgroup of order ?$n/k$? of ?$\\Gamma$?. Moreover, it is proved that ?$(k - 1)n$? is a sharp lower bound for the number of edges of a uniquely ?$k$?-colorable, noncomplete Cayley graph over an abelian group of order ?$n$?. Finally, we present constructions of uniquely colorable Cayley graphs by graph products"},{"@xml:lang":"sl","#text":"Pokažemo, da je kromatično število ?$\\chi (G) = k$? enolično pobarvljivega Cayleyevega grafa ?$G$? nad grupo ?$\\Gamma$? delitelj števila ?$|\\Gamma| = n$?. Vsak barvni razred v ?$k$?-barvanju grafa ?$G$? je odsek podgrupe reda ?$n/k$? grupe ?$\\Gamma$?. Še več, dokažemo da je ?$(k - 1)n$? ostra spodnja meja za število povezav enolično ?$k$?-pobarvljivega, nepolnega Cayleyjevega grafa nad abelovo grupo reda ?$n$?. Končno, predstavimo konstrukcije enolično pobarvljivega Cayleyjevega grafa z grafovskimi produkti"}],"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-UHT1IWT3","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-UHT1IWT3"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-UHT1IWT3/f7863ef4-930c-420a-ae51-b3b3412e52f7/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-UHT1IWT3/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-UHT1IWT3"}}}}