{"?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-C1KEUNTZ/aec9f275-99ae-47a9-b81b-786ee84962d0/PDF","dcterms:extent":"525 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-C1KEUNTZ/26c6a8a7-22bc-4a14-ad84-fac8f0e4b970/TEXT","dcterms:extent":"66 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-C1KEUNTZ/483cb8eb-273a-4c6c-a8b7-b2f5d9a56f40/PDF","dcterms:extent":"180 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-C1KEUNTZ/60de6d03-f3d3-4dd8-8752-41ec4e692d2c/TEXT","dcterms:extent":"6 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-C1KEUNTZ","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2023","dc:creator":["Kovič, Jurij","Pisanski, Tomaž","Zemljič, Sara Sabrina","Žitnik, Arjana"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:23"},{"@xml:lang":"sl","#text":"art. P1.01 (25 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.1970.29e","COBISSID_HOST:143319043","ISSN:1855-3966","URN:URN:NBN:SI:doc-C1KEUNTZ"],"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":"connectivity"},{"@xml:lang":"en","#text":"graph products"},{"@xml:lang":"en","#text":"planarity"},{"@xml:lang":"en","#text":"Sierpiński graphs"},{"@xml:lang":"en","#text":"symmetry"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"The Sierpiński product of graphs|"},"dc:description":{"@xml:lang":"sl","#text":"In this paper we introduce a product-like operation that generalizes the construction of the generalized Sierpiński graphs. Let ?$G, \\, H$? be graphs and let ?$f: V(G) \\to V(H)$? be a function. Then the Sierpiński product of graphs ?$G$? 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 ?$\\{g, g'\\}$? of ?$G?$ there is an edge between copies ?$gH$? and ?$g'H$? of form ?$\\{(g, f(g'), (g', f(g))\\}$?. Some basic properties of the Sierpiński product are presented. In particular, we show that the graph ?$G\\otimes_f H$? is connected if and only if both graphs ?$G$? and ?$H$? are connected and we present some conditions that ?$G, \\, H$? must fulfill for ?$G\\otimes_f H$? to be planar. As for symmetry properties, we show which automorphisms of ?$G$? and ?$H$? extend to automorphisms of ?$G\\otimes_f H$?. In several cases we can also describe the whole automorphism group of the graph ?$G\\otimes_f H$?. Finally, we show how to extend the Sierpiński product to multiple factors in a natural way. By applying this operation ?$n$? times to the same graph we obtain an alternative approach to the well-known ?$n$?-th generalized Sierpiński graph"},"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-C1KEUNTZ","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-C1KEUNTZ"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-C1KEUNTZ/aec9f275-99ae-47a9-b81b-786ee84962d0/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-C1KEUNTZ/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-C1KEUNTZ"}}}}