{"?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-JKXBZL5F/54fbcb04-8dbb-463b-ba45-ed614faa32bd/PDF","dcterms:extent":"292 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JKXBZL5F/b042264f-eaa0-4638-aa45-1ce8fcf98efa/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-JKXBZL5F","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":["López, S. C.","Muntaner-Batle, F. A."],"dc:format":[{"@xml:lang":"sl","#text":"letnik:12"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 235-245"}],"dc:identifier":["COBISSID:18120793","ISSN:1855-3966","URN:URN:NBN:SI:doc-JKXBZL5F"],"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":"Langfordovo zaporedje"},{"@xml:lang":"sl","#text":"zaporedja"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Distance labelings| a generalization of Langford sequences|"},"dc:description":[{"@xml:lang":"sl","#text":"A Langford sequence of order ?$m$? and defect ?$d$? can be identified with a labeling of the vertices of a path of order ?$2m$? in which each label from ?$d$? up to ?$d + m - 1$? appears twice and in which the vertices that have been labeled with ?$k$? are at distance ?$k$?. In this paper, we introduce two generalizations of this labeling that are related to distances. The basic idea is to assign nonnegative integers to vertices in such a way that if ?$n$? vertices ?$(n > 1)$? have been labeled with ?$k$? then they are mutually at distance ?$k$?. We study these labelings for some well known families of graphs. We also study the existence of these labelings in general. Finally, given a sequence or a set of nonnegative integers, we study the existence of graphs that can be labeled according to this sequence or set"},{"@xml:lang":"sl","#text":"Langfordovo zaporedje reda ?$m$? in defekta ?$d$? lahko identificiramo s številčenjem vozlišč poti reda ?$2m$?, pri katerem vsaka oznaka od ?$d$? do ?$d+ m - 1$? nastopa dvakrat, vozlišča označena s ?$k$? pa so na razdalji ?$k$?. V članku vpeljemo dve posplošitvi tega številčenja, ki sta povezani z razdaljami. Osnovna ideja je prirediti nenegativna cela števila vozliščem tako, da velja: če je ?$n$? vozlišč ?$(n > 1)$? označenih s ?$k$?, potem so ta med seboj na razdalji ?$k$?. Študiramo ta številčenja za nekatere dobro znane družine grafov. Študiramo tudi obstoj teh številčenj v splošnem. Nazadnje, če je dano zaporedje ali množica nenegativnih števil, študiramo obstoj grafov, ki jih lahko oštevilčimo v skladu s tem zaporedjem oziroma množico"}],"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-JKXBZL5F","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-JKXBZL5F"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-JKXBZL5F/54fbcb04-8dbb-463b-ba45-ed614faa32bd/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-JKXBZL5F/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-JKXBZL5F"}}}}