{"?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-IKJS1KN4/cdda13ad-2f8d-4942-b9ae-367ec1aa6370/PDF","dcterms:extent":"254 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-IKJS1KN4/2cab9892-f336-416b-9d33-0b52b7a515f4/TEXT","dcterms:extent":"11 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-IKJS1KN4","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2014","dc:creator":["Klisara, Jelena","Škrekovski, Riste"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:7"},{"@xml:lang":"sl","#text":"str. 293-297"}],"dc:identifier":["ISSN:1855-3966","COBISSID:2048233491","URN:URN:NBN:SI:doc-IKJS1KN4"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Društvo matematikov, fizikov in astronomov Slovenije"},"dc:subject":[{"@xml:lang":"en","#text":"cartesian product"},{"@xml:lang":"en","#text":"connectivity"},{"@xml:lang":"sl","#text":"grafi"},{"@xml:lang":"sl","#text":"kartezični produkt"},{"@xml:lang":"sl","#text":"povezanost"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"On the connectivity of Cartesian product of graphs|"},"dc:description":{"@xml:lang":"sl","#text":"We give a new alternative proof of Liouville's formula which states that for any graphs ?$G$? and ?$H$? on at least two vertices, ?$\\kappa(G \\Box H) = \\min\\{\\kappa(G)|H|, |G|\\kappa(H), \\delta(G) + \\delta(H)\\}$?, where ?$\\kappa$? and ?$\\delta$? denote the connectivity number and minimum degree of a given graph, respectively. The main idea of our proof is based on construction of a vertex-fan which connects a vertex from ?$V(G \\Box H)$? to a subgraph of ?$G \\Box H$?. We also discuss the edge version of this problem as well as formula for products with more than two factors"},"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-IKJS1KN4","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-IKJS1KN4"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-IKJS1KN4/cdda13ad-2f8d-4942-b9ae-367ec1aa6370/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-IKJS1KN4/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-IKJS1KN4"}}}}