{"?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-85TP6JEE/8d3df9a9-8613-42b4-b64e-c832063ff61e/PDF","dcterms:extent":"292 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-85TP6JEE/5941b474-cd52-4267-aada-cadeb4c1c87a/TEXT","dcterms:extent":"24 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-85TP6JEE","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":"Cichacz, Sylwia","dc:format":[{"@xml:lang":"sl","#text":"letnik:13"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 417-425"}],"dc:identifier":["COBISSID:18368345","ISSN:1855-3966","URN:URN:NBN:SI:doc-85TP6JEE"],"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":"abelska grupa"},{"@xml:lang":"sl","#text":"grupe"},{"@xml:lang":"sl","#text":"grupno razdaljno magično označevanje"},{"@xml:lang":"sl","#text":"razčlenitev s konstantno vsoto"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On zero sum-partition of Abelian groups into three sets and group distance magic labeling|"},"dc:description":[{"@xml:lang":"sl","#text":"We say that a finite abelian group ?$\\Gamma$? has the constant-sum-partition property into ?$t$? sets (CSP(?$t$?)-property) if for every partition ?$n = r_1+r_2+\\dots +r_t$? of ?$n$?, with ?$r_i \\geq 2$? for ?$2 \\leq i \\leq t$?, there is a partition of ?$\\Gamma$? into pairwise disjoint subsets ?$A_1 ,A_2, \\dots ,A_t$?, such that ?$A_i = r_i$? and for some ?$\\nu \\in \\Gamma$?, ?$\\sum_{a \\in A_i} a = \\nu$ for $1 \\leq i \\leq t$?. For ?$\\nu = g_0$? (where ?$g_0$? is the identity element of ?$\\Gamma$?) we say that ?$\\Gamma$? has zero-sum-partition property into ?$t$? sets (ZSP(?$t$?)-property). A ?$\\Gamma$?-distance magic labeling of a graph ?$G = (V,E)$? with ?$V = n$? is a bijection ?$\\ell$? from ?$V$? to an abelian group ?$\\Gamma$? of order ?$n$? such that the weight ?$w(x) = \\sum_{y\\in N(x)}\\ell(y)$? of every vertex ?$x \\in V$? is equal to the same element ?$\\mu \\in \\Gamma$?, called the magic constant. A graph ?$G$? is called a group distance magic graph if there exists a ?$\\Gamma$?-distance magic labeling for every abelian group ?$\\Gamma$? of order ?$V(G)$?. In this paper we study the CSP$(3)$-property of ?$\\Gamma$?, and apply the results to the study of group distance magic complete tripartite graphs"},{"@xml:lang":"sl","#text":"Pravimo, da ima končna abelska grupa ?$\\Gamma$? lastnost razčlenitve s konstantno vsoto v ?$t$? množic (CSP(?$t$?)-lastnost), če za vsako razčlenitev ?$n=r_1+r_2+\\dots +r_t$? števila ?$n$?, kjer je ?$2 \\leq i \\leq t$?, obstaja razčlenitev grupe ?$\\Gamma$? v paroma disjunktne podmnožice ?$A_1 ,A_2, \\dots ,A_t$?, tako da je ?$A_i = r_i$? in za nek ?$\\nu \\in \\Gamma$?, ?$\\sum_{a \\in A_i} a = \\nu$? za ?$1 \\leq i \\leq t$?. Za ?$\\nu = g_0$? (kjer je ?$g_0$? enotski element grupe ?$\\Gamma$?) pravimo, da ima ?$\\Gamma$? lastnost razčlenitve z ničelno vsoto v ?$t$? množic (ZSP(?$t$?)-lastnost). ?$\\Gamma$?-razdaljno magično označevanje grafa ?$G = (V,E)$? z $?V = n$? je takšna bijekcija ?$\\ell$? množice vozlišč ?$V$? na abelsko grupo ?$\\Gamma$? reda ?$n$?, pri kateri je utež ?$w(x) = \\sum_{y\\in N(x)}\\ell(y)$? vsakega vozlišča ?$x \\in V$? enaka istemu elementu ?$\\mu \\in \\Gamma$?, imenovanemu magična konstanta. Graf ?$G$? se imenuje grupno razdaljni magični graf, če obstaja ?$\\Gamma$?-razdaljno magično označevanje za vsako abelsko grupo ?$\\Gamma$? reda ?$V(G)$?. V tem članku raziskujemo CSP(3)-lastnost grupe ?$\\Gamma$?, potem pa uporabimo rezultate za študij grupno razdaljnih magičnih polnih tridelnih grafov"}],"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-85TP6JEE","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-85TP6JEE"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-85TP6JEE/8d3df9a9-8613-42b4-b64e-c832063ff61e/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-85TP6JEE/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-85TP6JEE"}}}}