{"?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-B37T9BE2/04444d2a-2513-4511-9c90-07dfb1b92a57/PDF","dcterms:extent":"378 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-B37T9BE2/f8105bad-8d20-4b9e-9510-89262aa9f536/TEXT","dcterms:extent":"43 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-B37T9BE2","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2024","dc:creator":["Henning, Michael A.","Klavžar, Sandi","Kleszcz, Elżbieta","Pilśniak, Monika"],"dc:format":[{"@xml:lang":"sl","#text":"16 str."},{"@xml:lang":"sl","#text":"letnik:24"},{"@xml:lang":"sl","#text":"številka:3, article  p3.06"}],"dc:identifier":["DOI:10.26493/1855-3974.2892.f07","ISSN:1855-3966","COBISSID_HOST:202296323","URN:URN:NBN:SI:doc-B37T9BE2"],"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":"dominacijsko število"},{"@xml:lang":"en","#text":"domination number"},{"@xml:lang":"sl","#text":"graf Sierpińskega"},{"@xml:lang":"en","#text":"Sierpiński domination number"},{"@xml:lang":"en","#text":"Sierpiński graph"},{"@xml:lang":"en","#text":"Sierpiński product"},{"@xml:lang":"sl","#text":"Sierpińskijev produkt"},{"@xml:lang":"sl","#text":"Sierpińskijevo dominacijsko število"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The Sierpiński domination number|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G$? and ?$H$? be graphs and let ?$f \\colon V(G)\\rightarrow V(H)$? be a function. The Sierpiński product of ?$G$? and ?$H$? with respect to ?$f$?, denoted by ?$G \\otimes _f H$?, is defined as the graph on the vertex set ?$V(G)\\times V(H)$?, consisting of ?$|V(G)|$? copies of ?$H$?; for every edge ?$gg'$? of ?$G$? there is an edge between copies ?$gH$? and ?$g'H$? of ?$H$? associated with the vertices ?$g$? and ?$g'$? of ?$G$?, respectively, of the form ?$(g,f(g'))(g',f(g))$?. In this paper, we define the Sierpiński domination number as the minimum of ?$\\gamma(G\\otimes _f H)$? over all functions ?$f \\colon V(G)\\rightarrow V(H)$?. The upper Sierpiński domination number is defined analogously as the corresponding maximum. After establishing general upper and lower bounds, we determine the upper Sierpiński domination number of the Sierpiński product of two cycles, and determine the lower Sierpiński domination number of the Sierpiński product of two cycles in half of the cases and in the other half cases restrict it to two values"},{"@xml:lang":"sl","#text":"Naj bosta ?$G$? in ?$H$? grafa ter naj bo funkcija ?$f \\colon V(G)\\rightarrow V(H)$?. Sierpińskijev produkt ?$G$? in ?$H$? glede na ?$f$?, označen z ?$G \\otimes _f H$?, je definiran kot graf na množici vozlišč ?$V(G)\\times V(H)$?, sestavljen iz ?$|V(G)|$? kopij ?$H$?; za vsako povezavo ?$gg'$? v ?$G$? obstaja povezava med kopijama ?$gH$? in ?$g'H$? v ?$H$?, prirejenimi vozliščema ?$g$? oziroma ?$g'$? v ?$G$?, v obliki ?$(g,f(g'))(g',f(g))$?. V tem članku definiramo Sierpińskijevo dominacijsko število kot minimum ?$\\gamma(G\\otimes _f H)$? nad vsemi funkcijami ?$f \\colon V(G)\\rightarrow V(H)$?. Zgornje Sierpińskijevo dominacijsko število je definirano analogno kot ustrezni maksimum. Po določitvi splošnih zgornjih in spodnjih mej določimo zgornje Sierpińskijevo dominacijsko število Sierpińskijevega produkta dveh ciklov in določimo spodnje Sierpińskijevo dominacijsko število Sierpińskijevega produkta dveh ciklov v polovici primerov ter ga v drugi polovici primerov omejimo na dve vrednosti"}],"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-B37T9BE2","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-B37T9BE2"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-B37T9BE2/04444d2a-2513-4511-9c90-07dfb1b92a57/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-B37T9BE2/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-B37T9BE2"}}}}