{"?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-WYZI63RO/38258e20-f682-41f3-9073-4411476de57c/PDF","dcterms:extent":"388 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-WYZI63RO/af9aaa43-2416-4899-a22b-89c6b7970348/TEXT","dcterms:extent":"35 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-WYZI63RO","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2015","dc:creator":["Anholcer, Marcin","Cichacz, Sylwia","Peterin, Iztok","Tepeh, Aleksandra"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 93-107"}],"dc:identifier":["COBISSID:17280857","ISSN:1855-3966","URN:URN:NBN:SI:doc-WYZI63RO"],"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":"Abelian group"},{"@xml:lang":"sl","#text":"Abelova grupa"},{"@xml:lang":"en","#text":"direct product of graphs"},{"@xml:lang":"sl","#text":"direktni produkt grafov"},{"@xml:lang":"en","#text":"distance magic labeling"},{"@xml:lang":"en","#text":"group labeling"},{"@xml:lang":"sl","#text":"grupno označevanje"},{"@xml:lang":"sl","#text":"razdaljno magično označevanje"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Group distance magic labeling of direct product of graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G = (V,E)$? be a graph and ?$\\Gamma$? an Abelian group, both of order ?$n$?. A group distance magic labeling of ?$G$? is a bijection ?$\\ell \\colon V \\rightarrow \\Gamma$? for which there exists ?$\\mu \\in \\Gamma$? such that ?$\\sum_{x \\in N(v)}\\ell (x) = \\mu $? for all ?$v \\in V$?, where ?$N(v)$? is the neighborhood of ?$v$?. In this paper we consider group distance magic labelings of direct product of graphs. We show that if ?$G$? is an ?$r$?-regular graph of order ?$n$? and ?$m = 4$? or ?$m = 8$? and ?$r$? is even, then the direct product ?$C_{m} \\times G$? ?$\\Gamma$?-distance magic for every Abelian group of order ?$mn$?. We also prove that ?$C_{m} \\times C_{n}$? is ?$\\mathbb{Z}_{mn}$?-distance magic if and only if ?$m \\in \\{4,8\\}$? or ?$n \\in \\{4,8\\}$? or ?$m,n \\equiv 0 \\pmod 4$?. It is also shown that if ?$m,n \\not\\equiv 0 \\pmod 4$? then ?$C_{m} \\times C_{n}$? is not ?$\\Gamma$?-distance magic for any Abelian group ?$\\Gamma$? of order ?$mn$?"},{"@xml:lang":"sl","#text":"Naj bo ?$G = (V,E)$? graf in ?$\\Gamma$? Abelova grupa, oba reda ?$n$?. Grupno razdaljno magično označevanje grafa ?$G$? je bijekcija ?$\\ell \\colon V \\rightarrow \\Gamma$?, za katero obstaja tak ?$\\mu \\in \\Gamma$?, da je ?$\\sum_{x\\in N(v)}\\ell (x) = \\mu$? za vsak ?$v \\in V$?, kjer je ?$N(v)$? soseščina vozlišča ?$v$?. V članku obravnavamo grupno razdaljno magično označevanje direktnih produktov grafov. Pokažemo, da če je ?$G$? ?$r$?-regularen graf reda ?$n$? in ?$m=4$? ali ?$m=8$? in je ?$r$? sodo število, potem je direktni produkt ?$C_{m} \\times G$? ?$\\Gamma$?-razdaljno magični graf za vsako Abelovo grupo reda ?$mn$?. Pokažemo tudi, da je ?$C_{m} \\times C_{n}$? ?$\\mathbb{Z}_{mn}$?-razdaljno magični graf natanko tedaj, ko je ?$m \\in \\{4,8\\}$? ali ?$n \\in \\{4,8\\}$? ali ?$m,n \\equiv 0 \\pmod 4$?. Prav tako pokažemo, da če ?$m,n \\not\\equiv 0 \\pmod 4$?, potem ?$C_{m}\\times C_{n}$? ni ?$\\Gamma$?-razdaljno magični graf za nobeno Abelovo grupo ?$\\Gamma$? reda ?$mn$?"}],"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-WYZI63RO","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-WYZI63RO"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-WYZI63RO/38258e20-f682-41f3-9073-4411476de57c/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-WYZI63RO/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-WYZI63RO"}}}}