{"?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-CWN748I8/fd91a02a-253e-42b8-915b-8169a04c613d/PDF","dcterms:extent":"302 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-CWN748I8/f7ae39b7-2ee3-4aba-a007-948d866abaaf/TEXT","dcterms:extent":"31 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-CWN748I8","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2019","dc:creator":["Brešar, Boštjan","Kos, Tim","Torres, Pablo"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:17"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 419-430"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:18789721","URN:URN:NBN:SI:doc-CWN748I8"],"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":"Grundy domination number"},{"@xml:lang":"en","#text":"Grundy total domination number"},{"@xml:lang":"sl","#text":"Grundyjevo celotno dominatno število"},{"@xml:lang":"sl","#text":"Grundyjevo dominantno število"},{"@xml:lang":"en","#text":"Kneser graph"},{"@xml:lang":"sl","#text":"Kneserjev graf"},{"@xml:lang":"en","#text":"minimum rank"},{"@xml:lang":"sl","#text":"najmanjši rang"},{"@xml:lang":"sl","#text":"število ničelne prisile"},{"@xml:lang":"en","#text":"zero forcing number"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Grundy domination and zero forcing in Kneser graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"In this paper, we continue the investigation of different types of (Grundy) dominating sequences. We consider four different types of Grundy domination numbers and the related zero forcing numbers, focusing on these numbers in the well-known class of Kneser graphs ?$K_{n,r}$?. In particular, we establish that the Grundy total domination number ?$\\gamma_{\\rm gr}^t(K_{n,r})$? equals ?${{2r}\\choose {r}}$? for any ?$r\\ge 2$? and ?$n\\ge 2r+1$?. For the Grundy domination number of Kneser graphs we get ?$\\gamma_{\\rm gr}(K_{n,r})=\\alpha(K_{n,r})$? whenever ?$n$? is sufficiently larger than ?$r$?. On the other hand, the zero forcing number ?$Z(K_{n,r})$? is proved to be ?${{n}\\choose{r}}-{{2r}\\choose{r}}$? when ?$n\\ge 3r+1$? and ?$r\\ge 2$?, while lower and upper bounds are provided for ?$Z(K_{n,r})$? when ?$2r+1\\le n\\le 3r$?. Some lower bounds for different types of minimum ranks of Kneser graphs are also obtained along the way"},{"@xml:lang":"sl","#text":"V članku nadaljujemo z raziskavami različnih tipov (Grundyjevih) dominacijskih zaporedij. Obravnavamo štiri različne tipe Grundyjevih dominantnih števil in njim sorodna števila ničelne prisile, pri čemer se osredotočamo na ta števila v dobro znanih Kneserjevih grafih ?$K_{n,r}$?. Med drugim ugotovimo, da je Grundyjevo celotno dominantno število ?$\\gamma_{\\rm gr}^t(K_{n,r})$? enako ?${{2r}\\choose {r}}$? za vsaka ?$r\\ge 2$? in ?$n\\ge 2r+1$?. Za Grundyjevo dominantno število Kneserjevega grafa dobimo, da je ?$\\gamma_{\\rm gr}(K_{n,r})=\\alpha(K_{n,r})$?, če je le ?$n$? dovolj veliko število v primerjavi z ?$r$?. Dokažemo tudi, da je število ničelne prisile ?$Z(K_{n,r})$? enako ?${{n}\\choose{r}}-{{2r}\\choose{r}}$?, ko je ?$n\\ge 3r+1$? in ?$r\\ge 2$?, medtem ko za ?$Z(K_{n,r})$?, ko je ?$2r+1\\le n\\le 3r$?, najdemo spodnje in zgornje meje. Spotoma dobimo tudi nekaj spodnjih mej za različne tipe najmanjših rangov Kneserjevih 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-CWN748I8","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-CWN748I8"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-CWN748I8/fd91a02a-253e-42b8-915b-8169a04c613d/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-CWN748I8/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-CWN748I8"}}}}