{"?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-U7TFO1K9/c9fd0ff1-44bc-4376-b28e-fdee5e111421/PDF","dcterms:extent":"304 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-U7TFO1K9/30201c15-aa92-4f8e-894f-371fa10ef8e6/TEXT","dcterms:extent":"14 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-U7TFO1K9","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":"Yero, Ismael G.","dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:9"},{"@xml:lang":"sl","#text":"str. 19-25"}],"dc:identifier":["COBISSID:17569369","ISSN:1855-3966","URN:URN:NBN:SI:doc-U7TFO1K9"],"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":"Cartesian product graph"},{"@xml:lang":"sl","#text":"dominacija"},{"@xml:lang":"en","#text":"domination"},{"@xml:lang":"sl","#text":"kartezični produktni graf"},{"@xml:lang":"sl","#text":"krepki produktni graf"},{"@xml:lang":"sl","#text":"parcialni produkt grafov"},{"@xml:lang":"en","#text":"partial product of graphs"},{"@xml:lang":"en","#text":"strong product graph"},{"@xml:lang":"sl","#text":"Vizingova domneva"},{"@xml:lang":"en","#text":"Vizing's conjecture"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Partial product of graphs and Vizing's conjecture|"},"dc:description":[{"@xml:lang":"sl","#text":"Let ?$G$? and ?$H$? be two graphs with vertex sets ?$V_1 = \\{u_1, \\dots, u_{n_1}\\}$? and ?$V_2 = \\{v_1, \\dots, u_{n_2}\\}$?, respectively. If ?$S \\subset V_2$?, then the partial Cartesian product of ?$G$? and ?$H$? with respect to ?$S$? is the graph ?$G \\Box_SH = (V,E)$?, where ?$V = V1 \\times V_2$? and two vertices ?$(u_i, v_j)$? and ?$(u_k,v_j)$? are adjacent in ?$G \\Box_SH$? if and only if either ?$(u_i = u_k \\text{ and } v_j \\sim v_l)$? or ?$(u_i \\sim u_k \\text{ and } v_j = v_l \\in S)$?. If ?$A \\subset V_1$? and ?$B \\subset V_2$?, then the restricted partial strong product of ?$G$? and ?$H$? with respect to ?$A$? and ?$B$? is the graph ?$G_A \\boxtimes_B H = (V,E)$?, where ?$V = V_1 \\times V_2$? and two vertices ?$(u_i, v_j)$? and ?$(u_k,v_l)$? are adjacent in ?$G_A \\boxtimes_B H$? if and only if either ?$(u_i = u_k \\text{ and } v_j \\sim v_l)$? or ?$(u_i \\sim u_k \\text{ and } v_j = v_l)$? or ?$(u_i \\in A, u_k \\notin A, v_j \\in B, v_l \\notin B, u_i \\sim u_k \\text{ and } v_j \\sim v_l)$? or ?$(u_i \\notin A, u_k \\in A, v_j \\notin B, v_l \\in B, u_i \\sim u_k \\text{ and } v_j \\sim v_l)$?. In this article we obtain Vizing-like results for the domination number and the independence domination number of the partial Cartesian product of graphs. Moreover we study the domination number of the restricted partial strong product of graphs"},{"@xml:lang":"sl","#text":"Naj bosta ?$G$? in ?$H$? dva grafa z množicama vozlišč ?$V_1 = \\{u_1, \\dots, u_{n_1}\\}$ in $V_2 = \\{v_1, \\dots, u_{n_2}\\}$?. Če je ?$S \\subset V_2$?, potem je parcialni kartezični produkt grafov ?$G$? in ?$H$? glede na ?$S$? graf ?$G \\Box_SH = (V,E)$?, kjer je ?$V = V1 \\times V_2$? in dve vozlišči ?$(u_i, v_j)$? in ?$(u_k,v_j)$? sta sosedni v ?$G \\Box_SH$? če in samo če je bodisi ?$(u_i = u_k \\text{ in } v_j \\sim v_l)$? ali ?$(u_i \\sim u_k \\text{ in } v_j = v_l \\in S)$?. Če je ?$A \\subset V_1$ in $B \\subset V_2$?, potem je zoženi parcialni krepki produkt grafov ?$G$? in ?$H$? glede na ?$A$? in ?$B$? graf ?$G_A \\boxtimes_B H = (V,E)$?, kjer je ?$V = V_1 \\times V_2$? in dve vozlišči ?$(u_i, v_j)$? and ?$(u_k,v_l)$? sta sosedni v ?$G_A \\boxtimes_B H$? če in samo če je bodisi ?$(u_i = u_k \\text{ in } v_j \\sim v_l)$? bodisi? $(u_i \\sim u_k \\text{ in } v_j = v_l)$? ali ?$(u_i \\in A, u_k \\notin A, v_j \\in B, v_l \\notin B, u_i \\sim u_k \\text{ in } v_j \\sim v_l)$? ali ?$(u_i \\notin A, u_k \\in A, v_j \\notin B, v_l \\in B, u_i \\sim u_k \\text{ in } v_j \\sim v_l)$?. V članku dobimo Vizingovim podobne rezultate za dominacijsko število parcialnega kartezičnega produkta grafov. Poleg tega študiramo dominacijsko število zoženega parcialnega krepkega produkta 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-U7TFO1K9","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-U7TFO1K9"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-U7TFO1K9/c9fd0ff1-44bc-4376-b28e-fdee5e111421/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-U7TFO1K9/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-U7TFO1K9"}}}}