{"?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-DQ0OK6VX/ceb4375d-166b-4a7d-b0bb-26598c0ee7e6/PDF","dcterms:extent":"262 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DQ0OK6VX/d66c52bd-55ea-4abd-8dd5-b6e62ff67e8e/TEXT","dcterms:extent":"19 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DQ0OK6VX/47eded6b-0a35-4065-8e3f-909576856bda/PDF","dcterms:extent":"139 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-DQ0OK6VX/e446912c-e93f-4d96-8424-95bd3c5d5ad1/TEXT","dcterms:extent":"3 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-DQ0OK6VX","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":["Sopena, Éric","Woźniak, Mariusz"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"P1.07 (7 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2144.9e3","COBISSID_HOST:149266179","ISSN:1855-3966","URN:URN:NBN:SI:doc-DQ0OK6VX"],"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":"arc-colouring"},{"@xml:lang":"sl","#text":"barvanje lokov"},{"@xml:lang":"sl","#text":"barvanje lokov, ki razlikuje sosede"},{"@xml:lang":"sl","#text":"digraf"},{"@xml:lang":"en","#text":"digraph"},{"@xml:lang":"en","#text":"neighbour-distinguishing arc-colouring"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A note on the neighbour-distinguishing index of digraphs|"},"dc:description":[{"@xml:lang":"sl","#text":"In this note, we introduce and study a new version of neighbour-distinguishing arc-colourings of digraphs. An arc-colouring ?$\\gamma$? of a digraph ?$D$? is proper if no two arcs with the same head or with the same tail are assigned the same colour. For each vertex ?$u$? of ?$D$?, we denote by ?$S_{\\gamma}^- (u)$? and ?$S_{\\gamma}^+ (u)$? the sets of colours that appear on the incoming arcs and on the outgoing arcs of ?$u$?, respectively. An arc colouring ?$\\gamma$? of ?$D$? is neighbour-distinguishing if, for every two adjacent vertices ?$u$? and ?$v$? of ?$D$?, the ordered pairs ?$(S_{\\gamma}^- (u), S_{\\gamma}^+(u))$? and ?$(S_{\\gamma}^- (v), S_{\\gamma}^+ (v))$? are distinct. The neighbour-distinguishing index of ?$D$? is then the smallest number of colours needed for a neighbour-distinguishing arc-colouring of ?$D$?. We prove upper bounds on the neighbour-distinguishing index of various classes of digraphs"},{"@xml:lang":"sl","#text":"V članku vpeljemo in preučujemo novo različico barvanja lokov v digrafih, ki razlikuje sosede. Barvanje lokov ?$\\gamma$? digrafa ?$D$? je pravilno, če nobenima dvema lokoma z istim koncem ali z istim začetkom ni dodeljena ista barva. Za vsako vozlišče ?$u$? digrafa ?$D$? označimo z ?$S_{\\gamma}^- (u)$? in ?$S_{\\gamma}^+ (u)$? množici barv, ki nastopata na vhodnih lokih in na izhodnih lokih vozlišča ?$u$?. Barvanje lokov ?$\\gamma$? digrafa ?$D$? razlikuje sosede, če sta za vsaka dva sosedna vozlišča ?$u$? in ?$v$? digrafa ?$D$?, urejena para ?$(S_{\\gamma}^- (u), S_{\\gamma}^ + (u))$? in ?$(S_{\\gamma}^- (v), S_{\\gamma}^+ (v))$? različna. Indeks razlikovanja sosedov digrafa ?$D$? je potem najmanjše število barv, ki so potrebne za barvanje lokov, ki razlikuje sosede v digrafu ?$D$?. Dokažemo zgornje meje za indeks razlikovanja sosedov različnih razredov digrafov"}],"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-DQ0OK6VX","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-DQ0OK6VX"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-DQ0OK6VX/ceb4375d-166b-4a7d-b0bb-26598c0ee7e6/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-DQ0OK6VX/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-DQ0OK6VX"}}}}