{"?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-567RMQIX/4f651ab9-18b9-448d-9dba-fcb00308517f/PDF","dcterms:extent":"270 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-567RMQIX/b2fe36c5-241a-46c6-a8f7-0c9af2b43da5/TEXT","dcterms:extent":"30 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-567RMQIX","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":"Grech, Mariusz","dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:21"},{"@xml:lang":"sl","#text":"str. 259-269"}],"dc:identifier":["DOI:10.26493/1855-3974.1926.6ad","COBISSID_HOST:112755971","ISSN:1855-3966","URN:URN:NBN:SI:doc-567RMQIX"],"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":"automorphism group"},{"@xml:lang":"en","#text":"colored graph"},{"@xml:lang":"en","#text":"direct product"},{"@xml:lang":"sl","#text":"grupa avtomorfizmov"},{"@xml:lang":"sl","#text":"kartezični produkt"},{"@xml:lang":"sl","#text":"permutacijska grupa"},{"@xml:lang":"en","#text":"permutation group"},{"@xml:lang":"sl","#text":"pobarvan graf"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Decompositions of the automorphism groups of edge-colored graphs into the direct product of permutation groups|"},"dc:description":[{"@xml:lang":"sl","#text":"In the paper Graphical complexity of products of permutation groups, M. Grech, A. Jeż, and A. Kisielewicz have proved that the direct product of automorphism groups of edgecolored graphs is itself the automorphism group of an edge-colored graph. In this paper, we study the direct product of two permutation groups such that at least one of them fails to be the automorphism group of an edge-colored graph. We find necessary and sufficient conditions for the direct product to be the automorphism group of an edge-colored graph. The same problem is settled for the edge-colored digraphs"},{"@xml:lang":"sl","#text":"V članku Graphical complexity of products of permutation groups, so M. Grech, A. Jeż in A. Kisielewicz dokazali, da je kartezični produkt grup avtomorfizmov grafov s pobarvanimi povezavami tudi sam grupa avtomorfizmov nekega grafa s pobarvanimi povezavami. V članku raziskujemo kartezični produkt dveh permutacijskih grup, od katerih vsaj ena ni grupa avtomorfizmov nobenega grafa s pobarvanimi povezavami. Poiščemo potrebne in zadostne pogoje za to, da je tak kartezični produkt grupa avtomorfizmov nekega grafa s pobarvanimi povezavami. Isti problem rešimo tudi za usmerjene grafe s pobarvanimi povezavami"}],"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-567RMQIX","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-567RMQIX"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-567RMQIX/4f651ab9-18b9-448d-9dba-fcb00308517f/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-567RMQIX/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-567RMQIX"}}}}