{"?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-JR7GQZUD/b02789d0-d597-4cd0-85c5-b7c9e2e32e11/PDF","dcterms:extent":"302 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-JR7GQZUD/8d43a1c8-e69c-4440-9c84-57b0ad55f4bd/TEXT","dcterms:extent":"39 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-JR7GQZUD","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Héger, Tamás","Hernandez Lucas, Lisa"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"str. 61-76"}],"dc:identifier":["ISSN:1855-3974","COBISSID_HOST:43094787","URN:URN:NBN:SI:doc-JR7GQZUD"],"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":"dominating set"},{"@xml:lang":"sl","#text":"dominirajoča množica"},{"@xml:lang":"en","#text":"finite generalized quadrangle"},{"@xml:lang":"sl","#text":"končni posplošeni pravokotnik"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Dominating sets in finite generalized quadrangles|"},"dc:description":[{"@xml:lang":"sl","#text":"A dominating set in a graph is a set of vertices such that each vertex not in the set has a neighbor in the set. The domination number is the smallest size of a dominating set. We consider this problem in the incidence graph of a generalized quadrangle. We show that the domination number of a generalized quadrangle with parameters ?$s$? and ?$t$? is at most ?$2st+1$?, and we prove that this bound is sharp if ?$s=t$? or if ?$s=q-1$? and ?$t=q+1$?. Moreover, we give a complete classification of smallest dominating sets in generalized quadrangles where ?$s=t$?, and give some general results for small dominating sets in the general case"},{"@xml:lang":"sl","#text":"Dominirajoča množica v grafu je množica točk z lastnostjo, da ima vsaka točka, ki ni vsebovana v njej, vsaj eno sosedno točko v tej množici. Dominacijsko število je najmanjša velikost dominirajoče množice. Problem njegove določitve obravnavamo v incidenčnem grafu posplošenega pravokotnika. Pokažemo, da je dominacijsko število posplošenega pravokotnika s parametroma ?$s$? in ?$t$? največ ?$2st+1$?, in dokažemo, da je ta meja ostra, če je ?$s=t$? ali če je ?$s=q-1$? in ?$t=q+1$?. Poleg tega predstavimo popolno klasifikacijo najmanjših dominacijskih množic v posplošenih pravokotnikih, za katere je ?$s=t$?, pa tudi nekaj rezultatov za majhne dominacijske množice v splošnem primeru"}],"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-JR7GQZUD","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-JR7GQZUD"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-JR7GQZUD/b02789d0-d597-4cd0-85c5-b7c9e2e32e11/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-JR7GQZUD/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-JR7GQZUD"}}}}