{"?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-5JWYIMXY/aeef2bb9-8865-44f9-bc4c-3133b5c701af/PDF","dcterms:extent":"410 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-5JWYIMXY/0b21d98f-b093-4f4a-bdde-4b2584da123f/TEXT","dcterms:extent":"22 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-5JWYIMXY","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":"Zhou, Jin-Xin","dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:8"},{"@xml:lang":"sl","#text":"str. 235-244"}],"dc:identifier":["COBISSID:17372505","ISSN:1855-3966","URN:URN:NBN:SI:doc-5JWYIMXY"],"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":"direct product"},{"@xml:lang":"sl","#text":"direktni produkt"},{"@xml:lang":"en","#text":"super connectivity"},{"@xml:lang":"sl","#text":"super povezanost"},{"@xml:lang":"en","#text":"vertex-cut"},{"@xml:lang":"sl","#text":"vozliščni rez"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Super connectivity of direct product of graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"For a graph ?$G$?, ?$\\kappa(G)$? denotes its connectivity. A graph ?$G$? is super connected, or simply super-?$\\kappa$?, if every minimum separating set is the neighborhood of a vertex of ?$G$?, that is, every minimum separating set isolates a vertex. The direct product ?$G_1 \\times G_2$? of two graphs ?$G_1$? and ?$G_2$? is a graph with vertex set ?$V(G_1 \\times G_2) = V(G_1) \\times V(G_2)$? and edge set ?$E(G_1 \\times G_2) = \\{(u_1, v_1)(u_2, v_2) \\vert u_1u_2 \\in E(G1), v_1v_2 \\in E(G2)\\}$?. Let ?$\\Gamma = G \\times K_n$?, where ?$G$? is a non-trivial graph and ?$K_n(n \\ge 3)$? is a complete graph on ?$n$? vertices. In this paper, we show that ?$\\Gamma$? is not super-?$\\kappa$? if and only if either ?$\\kappa(\\Gamma) = n\\kappa(G)$?, or ?$\\Gamma \\cong K_{\\ell, \\ell} \\times K_3(\\ell > 0)$?"},{"@xml:lang":"sl","#text":"Za graf ?$G$? naj ?$\\kappa(G)$? označuje njeno povezanost. Graf ?$G$? je super povezan, ali na kratko super-?$\\kappa$?, če je vsaka minimalna separirajoča množica okolica vozlišča iz ?$G$?, to pomeni, da vsaka minimalna separirajoča množica izolira neko vozlišče. Direktni produkt ?$G_1 \\times G_2$? grafov ?$G_1$? in ?$G_2$? je graf z množico vozlišč ?$V(G_1 \\times G_2) = V(G_1) \\times V(G_2)$? in množico povezav ?$E(G_1 \\times G_2) = \\{(u_1, v_1)(u_2, v_2) \\vert u_1u_2 \\in E(G1), v_1v_2 \\in E(G2)\\}$?. Naj bo ?$\\Gamma = G \\times K_n$?, kjer je ?$G$? netrivialen graf in ?$K_n(n \\ge 3)$? poln graf na ?$n$? vozliščih. V tem članku pokažemo, da ?$\\Gamma$? ni super-?$\\kappa$?, če in samo če je bodisi ?$\\kappa(\\Gamma) = n\\kappa(G)$? bodisi je ?$\\Gamma \\cong K_{\\ell, \\ell} \\times K_3(\\ell > 0)$?"}],"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-5JWYIMXY","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-5JWYIMXY"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-5JWYIMXY/aeef2bb9-8865-44f9-bc4c-3133b5c701af/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-5JWYIMXY/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-5JWYIMXY"}}}}