{"?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-492BJFR6/9fa33053-4d48-468a-b1bf-97af918e1308/PDF","dcterms:extent":"331 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-492BJFR6/570dba1c-f822-46ec-abfe-7fda0fef5a8a/TEXT","dcterms:extent":"30 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-492BJFR6/50c59835-4ed1-4bf3-ab50-96d822a610ff/PDF","dcterms:extent":"177 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-492BJFR6/f42fc99a-5144-45b7-9bad-be11025a043a/TEXT","dcterms:extent":"3 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-492BJFR6","dcterms:issued":"2026","dc:creator":"Cichacz, Sylwia","dc:format":[{"@xml:lang":"sl","#text":"številka:2, article  p2.09"},{"@xml:lang":"sl","#text":"letnik:26"},{"@xml:lang":"sl","#text":"str. 1-10"}],"dc:identifier":["DOI:10.26493/1855-3974.3380.cb8","ISSN:1855-3974","COBISSID_HOST:289328387","URN:URN:NBN:SI:doc-492BJFR6"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem"},"dc:source":{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"},"dc:subject":[{"@xml:lang":"en","#text":"directed graph"},{"@xml:lang":"en","#text":"finite Abelian group"},{"@xml:lang":"sl","#text":"končne abelove grupe"},{"@xml:lang":"sl","#text":"množiče z ničelno vsoto"},{"@xml:lang":"sl","#text":"usmerjen graf"},{"@xml:lang":"en","#text":"zero-sum sets"}],"dc:title":{"@xml:lang":"sl","#text":"Irregular graph labelings in Abelian groups|"},"dc:description":[{"@xml:lang":"sl","#text":"Let G? = (V,E) be a directed graph of order n. If there exists a mapping ? from E(G?) to an Abelian group ? such that if we define a mapping ?_? from V(G?) to ? by ?_?(x) = ?y ? N?(x)?(xy) - ?y ? N?(x)?(yx),   (x ? V(G?)), then ?? is injective, then such a labeling ? is called ?-irregular. Recently it was showed that if n is large enough then G? has a ?-irregular labeling for any ? such that |?| > (1 + ?)n (in the paper from Cichacz and Tuza from 2022). In this paper, we prove that if all weakly connected components of G? are of size at least 4, then G? has a ?-irregular labeling for any finite group ? such that |?| >= n + 5"},{"@xml:lang":"sl","#text":"Naj bo G? = (V,E) usmerjen graf reda n. Če obstaja preslikava ? iz E(G?) v abelovo grupo ?, tako da je preslikava ?_? iz V(G?) v ? definirana z ?_?(x) = ?y ? N?(x)?(xy) - ?y ? N?(x)?(yx),   (x ? V(G?)), injektivna, preslikavo ? imenujemo ?-neregularna. Nedavno je bilo pokazano, da če je n dovolj velik, potem ima G? ?-neregularno označanje za vsako grupo ?, za katero velja |?| > (1 + ?)n (v članku Cichacza in Tuze iz leta 2022). V tem članku pokažemo, da če imajo vse šibko povezane komponente grafa G? velikost vsaj 4, potem ima G? ?-neregularno označanje za vsako končno grupo ?, za katero velja |?| ? n + 5"}],"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-492BJFR6","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-492BJFR6"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-492BJFR6/9fa33053-4d48-468a-b1bf-97af918e1308/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-492BJFR6/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-492BJFR6"}}}}