{"?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-1VA4YAXC/583d5746-5136-4a40-bb63-a98f5988249b/PDF","dcterms:extent":"448 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-1VA4YAXC/e76c5024-9c6b-44f9-917d-52c88beba7e9/TEXT","dcterms:extent":"56 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-1VA4YAXC","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2022","dc:creator":["Gorzkowska, Aleksandra","Henning, Michael A.","Pilśniak, Monika","Tumidajewicz, Elżbieta"],"dc:format":[{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"letnik:22"},{"@xml:lang":"sl","#text":"P2.04 (18 str.)"}],"dc:identifier":["DOI:10.26493/1855-3974.2522.eb3","COBISSID_HOST:116313603","ISSN:1855-3966","URN:URN:NBN:SI:doc-1VA4YAXC"],"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":"paired domination"},{"@xml:lang":"en","#text":"paired domination stability"},{"@xml:lang":"sl","#text":"parna dominacija"},{"@xml:lang":"sl","#text":"stabilnost parne dominacije"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Paired domination stability in graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"A set ?$S$? of vertices in a graph ?$G$? is a paired dominating set if every vertex of ?$G$? is adjacent to a vertex in ?$S$? and the subgraph induced by ?$S$? contains a perfect matching (not necessarily as an induced subgraph). The paired domination number, ?$\\gamma_{\\mathrm{pr}} (G)$?, of ?$G$? is the minimum cardinality of a paired dominating set of ?$G$?. A set of vertices whose removal from ?$G$? produces a graph without isolated vertices is called a non-isolating set. The minimum cardinality of a non-isolating set of vertices whose removal decreases the paired domination number is the ?$\\gamma_{\\mathrm{pr}}^-$?-stability of ?$G$?, denoted ?$\\mathrm{st}_{\\gamma_{\\mathrm{pr}}}^- (G)$?. The paired domination stability of ?$G$? is the minimum cardinality of a non-isolating set of vertices in ?$G$? whose removal changes the paired domination number. We establish properties of paired domination stability in graphs. We prove that if ?$G$? is a connected graph with ?$\\gamma_{\\mathrm{pr}} (G) \\geq 4$?, then ?$\\mathrm{st}_{\\gamma_{\\mathrm{pr}}}^- (G) \\leq 2\\Delta (G)$? where ?$\\Delta (G)$? is the maximum degree in ?$G$?, and we characterize the infinite family of trees that achieve equality in this upper bound"},{"@xml:lang":"sl","#text":"Množica ?$S$? vozlišč grafa ?$G$? je parna dominacijska množica, če je vsako vozlišče grafa ?$G$? sosedno nekemu vozlišču iz množice ?$S$? in če podgraf, induciran z množico ?$S$?, vsebuje popolno prirejanje (ne nujno kot induciran podgraf). Parno dominacijsko število, ?$\\gamma_{\\mathrm{pr}} (G)$?, grafa ?$G$? je minimalna moč parne dominacijske množice grafa ?$G$?. Množica vozlišč, katerih odstranitev iz ?$G$? nam da graf brez izoliranih vozlišč, se imenuje neizolativna množica. Minimalna moč neizolativne množice vozlišč, katerih odstranitev zmanjša parno dominacijsko število, je ?$\\gamma_{\\mathrm{pr}}^-$?-stabilnost grafa ?$G$?, označena z ?$\\mathrm{st}_{\\gamma_{\\mathrm{pr}}}^- (G)$?. Stabilnost parne dominacije grafa ?$G$? je minimalna moč neizolativne množice vozlišč iz ?$G$?, katerih odstranitev spremeni parno dominacijsko število. Določimo lastnosti stabilnosti parne dominacije v grafih. Dokažemo: če je ?$G$? povezan graf in je ?$\\gamma_{\\mathrm{pr}} (G) \\geq 4$?, potem je ?$\\mathrm{st}_{\\gamma_{\\mathrm{pr}}}^- (G) \\leq 2\\Delta (G)$?, kjer je ?$\\Delta (G)$? maksimalna stopnja vozlišč v grafu ?$G$?; karakteriziramo tudi neskončno družino dreves, za katere v tej zgornji meji velja enakost"}],"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-1VA4YAXC","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-1VA4YAXC"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-1VA4YAXC/583d5746-5136-4a40-bb63-a98f5988249b/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-1VA4YAXC/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-1VA4YAXC"}}}}