{"?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-TNBZMBHJ/9067f9af-0533-43bc-bf98-1233de03c226/PDF","dcterms:extent":"377 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-TNBZMBHJ/d53e6724-a55c-4beb-a31f-94765302273f/TEXT","dcterms:extent":"22 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-TNBZMBHJ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Balachandran, Niranjan","Padinhatteeri, Sajith","Spiga, Pablo"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"str. 311-318"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18956121","URN:URN:NBN:SI:doc-TNBZMBHJ"],"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":"Cayley graphs"},{"@xml:lang":"sl","#text":"Cayleyjevi grafi"},{"@xml:lang":"en","#text":"distinguishing chromatic number"},{"@xml:lang":"sl","#text":"razločevalno kromatčno število"},{"@xml:lang":"en","#text":"vertex transitive graphs"},{"@xml:lang":"sl","#text":"vozliščno tranzitivni grafi"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Vertex transitive graphs G with chisub D(G) greater then chi(G) and small automorphism group|"},"dc:description":[{"@xml:lang":"sl","#text":"For a graph ?$G$? and a positive integer ?$k$?, a vertex labelling ?$f: V(G) \\rightarrow \\{1, 2, \\dots, k\\}$? is said to be ?$k$?-distinguishing if no non-trivial automorphism of ?$G$? preserves the sets ?$f^{-1}(i)$? for each ?$i \\in \\{1, \\dots, k\\}$?. The distinguishing chromatic number of a graph ?$G$?, denoted ?$\\chi_D(G)$?, is defined as the minimum ?$k$? such that there is a ?$k$?-distinguishing labelling of ?$V(G)$? which is also a proper coloring of the vertices of ?$G$?. In this paper, we prove the following theorem: Given ?$k \\in \\mathbb{N} $?, there exists an infinite sequence of vertex-transitive graphs ?$G_i = (V_i, E_i)$? such that (1.) ?$\\chi_D (G_i) > \\chi (G_i) > k$?, and (2.) ?$|\\rm{Aut}(G_i)| < 2k|V_i|$?, where ?$\\rm{Aut}(G_i)$? denotes the full automorphism group of ?$G_i$?. In particular, this answers a question posed by the first and second authors of this paper"},{"@xml:lang":"sl","#text":"Za graf ?$G$? in pozitivno celo število ?$k$? se označitev vozlišč ?$f: V(G) \\rightarrow \\{1, 2, \\dots, k\\}$? imenuje ?$k$?-razločevalna, če noben netrivialen avtomorfizem grafa ?$G$? ne ohranja množic ?$f^{-1}(i)$? za vsak ?$i \\in \\{1, \\dots, k\\}$?. Razločevalno kromatično število grafa ?$G$?, označeno z ?$\\chi_D(G)$?, je definirano kot najmanjše število ?$k$?, pri katerem obstaja ?$k$?-razločevalna označitev ?$V(G)$?, ki je tudi pravilno barvanje vozlišč grafa ?$G$?. V članku dokažemo naslednji izrek: Pri danem ?$k \\in \\mathbb{N}$? obstaja neskončno zaporedje vozliščno tranzitivnih grafov ?$G_i = (V_i, E_i)$?, za katere je (1.) ?$\\chi_D (G_i) > \\chi (G_i) > k$? in (2.) ?$|\\rm{Aut}(G_i)| < 2k|V_i|$?, kjer ?$\\rm{Aut}(G_i)$? označuje polno grupo avtomorfizmov grafa ?$G_i$?. To tudi odgovori na vprašanje, ki sta ga zastavila prvi in drugi avtor tega članka"}],"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-TNBZMBHJ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-TNBZMBHJ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-TNBZMBHJ/9067f9af-0533-43bc-bf98-1233de03c226/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-TNBZMBHJ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-TNBZMBHJ"}}}}