{"?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-X3HHSNAG/26096ef8-823c-4561-bbfb-044b8f227569/PDF","dcterms:extent":"370 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-X3HHSNAG/99102ba3-e8f0-46c7-a443-4192eac91d72/TEXT","dcterms:extent":"51 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-X3HHSNAG","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":["Henning, Michael A.","Peterin, Iztok"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 359-375"}],"dc:identifier":["COBISSID_HOST:18544217","ISSN:1855-3966","URN:URN:NBN:SI:doc-X3HHSNAG"],"dc:language":"en","dc:publisher":{"@xml:lang":"sl","#text":"Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije"},"dc:subject":[{"@xml:lang":"sl","#text":"celostno dominacijsko število"},{"@xml:lang":"en","#text":"disjoint total dominating sets"},{"@xml:lang":"sl","#text":"disjunktni celostni dominacijski množici"},{"@xml:lang":"en","#text":"total domination number"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"A characterization of graphs with disjoint total dominating sets|"},"dc:description":[{"@xml:lang":"sl","#text":"A set ?$S$? of vertices in a graph ?$G$? is a total dominating set of ?$G$? if every vertex is adjacent to a vertex in ?$S$?. A fundamental problem in total domination theory in graphs is to determine which graphs have two disjoint total dominating sets. In this paper, we solve this problem by providing a constructive characterization of the graphs that have two disjoint total dominating sets. Our characterization gives an entirely new description of graphs with two disjoint total dominating sets and places them in another context, developing them from four base graphs and applies a sequence of operations from seventeen operations that are independent and necessary to produce all such graphs. We show that every graph with two disjoint total dominating sets can be constructed using this method"},{"@xml:lang":"sl","#text":"Podmnožica vozlišč ?$S$? v grafu ?$G$? je celostna dominirajoča množica grafa ?$G$?, če je vsako vozlišče grafa ?$G$? sosednje kakemu vozlišču iz ?$S$?. Temeljni problem v celostni dominaciji grafov je ali za dan graf obstajata disjunktni celostni dominacijski množici. V tem delu je predstavljena rešitev omenjenega problema z konstrukcijsko karakterizacijo vseh grafov, ki imajo disjunktni celostni dominacijski množici. Ta karakterizacija postavi grafe z disjunktnima celostnima dominacijskima množicama v nov kontekst, kjer jih razvijemo iz štirih baznih grafov in zaporedno uporabo sedemnajstih operacij, ki so med seboj neodvisne in hkrati potrebne da opišemo vse take grafe. Pokažemo, da lahko vsak graf, ki vsebuje disjunktni celostni dominacijski množici lahko skonstruiramo s to metodo"}],"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-X3HHSNAG","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-X3HHSNAG"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-X3HHSNAG/26096ef8-823c-4561-bbfb-044b8f227569/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-X3HHSNAG/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-X3HHSNAG"}}}}