{"?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-68L993FA/c8696d13-c1d5-4612-8aa8-fabb829a3cd1/PDF","dcterms:extent":"402 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-68L993FA/c494d8d8-560b-4ffc-bca0-74a9615d445d/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-68L993FA","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":["Bujtás, Csilla","Jakovac, Marko"],"dc:format":[{"@xml:lang":"sl","#text":"številka:1"},{"@xml:lang":"sl","#text":"letnik:16"},{"@xml:lang":"sl","#text":"str. 183-202"}],"dc:identifier":["ISSN:1855-3966","COBISSID_HOST:24318728","URN:URN:NBN:SI:doc-68L993FA"],"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":"annihilation number"},{"@xml:lang":"en","#text":"block graph"},{"@xml:lang":"sl","#text":"bločni graf"},{"@xml:lang":"en","#text":"cactus graph"},{"@xml:lang":"sl","#text":"indeks popolne prevlade"},{"@xml:lang":"sl","#text":"indeks uničenja"},{"@xml:lang":"sl","#text":"kaktusni graf"},{"@xml:lang":"en","#text":"total domination number"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Relating the total domination number and the annihilation number of cactus graphs and block graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"The total domination number ?$\\gamma_t(G)$? of a graph ?$G$? is the order of a smallest set ?$D \\subseteq V(G)$? such that each vertex of ?$G$? is adjacent to some vertex in ?$D$?. The annihilation number ?$a(G)$? of ?$G$? is the largest integer ?$k$? such that there exist ?$k$? different vertices in ?$G$? with degree sum of at most ?$|E(G)|$?. It is conjectured that ?$\\gamma_t(G) \\leq a(G) + 1$? holds for every nontrivial connected graph ?$G$?. The conjecture was proved for graphs with minimum degree at least 3, and remains unresolved for graphs with minimum degree 1 or 2. In this paper we establish the conjecture for cactus graphs and block graphs"},{"@xml:lang":"sl","#text":"Indeks popolne prevlade ?$\\gamma_t(G)$? grafa ?$G$? je red najmanjše množice ?$D \\subseteq V(G)$?, za katero velja, da je vsako vozlišče grafa ?$G$? sosedno kakšnemu vozlišču grafa ?$D$?. Indeks uničenja ?$a(G)$? grafa ?$G$? je največje celo število ?$k$?, za katerega obstaja ?$k$? različnih vozlišč v ?$G$?, ki ustrezajo pogoju, da je vsota njihovih stopenj največ ?$|E(G)|$?. Domneva se, da neenakost ?$\\gamma_t(G) \\leq a(G) + 1$? velja za vsak netrivialen povezan graf ?$G$?. Ta domneva je bila dokazana za grafe, pri katerih je minimalna stopnja njihovih vozlišč najmanj 3, njen status pa ostaja nerazrešen za grafe, pri katerih je minimalna stopnja njihovih vozlišč 1 ali 2. V članku potrdimo njeno veljavnost za kaktusne grafe in bločne grafe"}],"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-68L993FA","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-68L993FA"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-68L993FA/c8696d13-c1d5-4612-8aa8-fabb829a3cd1/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-68L993FA/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-68L993FA"}}}}