{"?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-4XHO3CGN/c8-c485ce4-4aea58e8-5a22d1cfbf1ae4e-/PDF","dcterms:extent":"475 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-4XHO3CGN/e8b554fa-b073-4f38-bfcb-ab7696377270/TEXT","dcterms:extent":"37 KB"}],"edm:TimeSpan":{"@rdf:about":"2014-2024","edm:begin":{"@xml:lang":"en","#text":"2014"},"edm:end":{"@xml:lang":"en","#text":"2024"}},"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:doc-4XHO3CGN","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-OE00UKYR"},{"@xml:lang":"sl","#text":"Matrika"}],"dcterms:issued":"2023","dc:creator":"Prešeren, Ana Julija","dc:format":[{"@xml:lang":"sl","#text":"letnik:10"},{"@xml:lang":"sl","#text":"13 str."},{"@xml:lang":"sl","#text":"številka:2"}],"dc:identifier":["COBISSID_HOST:166247939","ISSN:2385-8567","URN:URN:NBN:SI:doc-4XHO3CGN"],"dc:language":"sl","dc:publisher":{"@xml:lang":"sl","#text":"Založba Fakultete za matematiko in fiziko Univerze v Ljubljani"},"dc:subject":[{"@xml:lang":"en","#text":"bondage edge set"},{"@xml:lang":"en","#text":"bondage number"},{"@xml:lang":"sl","#text":"dominantna množica"},{"@xml:lang":"sl","#text":"dominantno število"},{"@xml:lang":"en","#text":"dominating set"},{"@xml:lang":"en","#text":"domination number"},{"@xml:lang":"sl","#text":"krepki produkt"},{"@xml:lang":"sl","#text":"kritična množica povezav"},{"@xml:lang":"sl","#text":"povezavno kritično število"},{"@xml:lang":"en","#text":"strong product"}],"dcterms:temporal":{"@rdf:resource":"2014-2024"},"dc:title":{"@xml:lang":"sl","#text":"Dominacija v krepkih produktih polnih grafov in poti|"},"dc:description":[{"@xml:lang":"sl","#text":"A dominating set of a graph ?$G$? is a subset of ?$V(G)$? with the property, that every vertex of graph ?$G$? is either in this set or is adjacent to the vertex in it. The domination number ?$\\gamma(G)$? of a graph ?$G$? is the cardinality of a smallest dominating set. In this thesis we find the exact value of the domination number of the strong product of a complete graph with a path. It is not dependent on the order of the complete graph and is equal to ?$\\gamma(K_m \\boxtimes P_n) = \\lceil \\frac{n}{3} \\rceil$?. A bondage edge set of a graph ?$G$? is a subset of ?$E(G)$?, whose removal from ?$G$? results in a graph with the domination number greater than that of ?$G$?. The bondage number ?$b(G)$? is the cardinality of a smallest bondage edge set. It is a parameter to measure the vulnerability of a communication network under link failure. The bondage number of the strong product of a complete graph with a path depends on the order of the complete graph and the value of ?$n \\pmod{3}$?. For integers ?$m$? and ?$n$?, where ?$m\\geq 1$? and ?$n \\geq 2$?, ?$b(K_m \\boxtimes P_n)=\\lceil \\frac{m}{2} \\rceil$? if ?$n\\equiv 0 \\pmod{3}$?, ?$b(K_m \\boxtimes P_n)=\\lceil \\frac{3m}{2} \\rceil$? if ?$n\\equiv 1 \\pmod{3}$? and ?$b(K_m \\boxtimes P_n)=m$? if ?$n\\equiv 2 \\pmod{3}$?"},{"@xml:lang":"sl","#text":"Dominantna množica grafa ?$G$? je podmnožica množice vozlišč ?$V(G)$?, za katero velja, da je vsako vozlišče grafa ?$G$? prisotno v tej množici ali pa je sosedno vozlišču v njej. Dominantno število grafa, označujemo ga z ?$\\gamma(G)$?, je kardinalnost dominantne množice najmanjše moči. V delu poiščemo točno vrednost dominantnega števila krepkega produkta polnega grafa in poti. Njegova vrednost je neodvisna od velikosti polnega grafa in je enaka ?$\\gamma(K_m \\boxtimes P_n) = \\lceil \\frac{n}{3} \\rceil$?. Kritična množica povezav grafa ?$G$? je podmnožica množice povezav ?$E(G)$?, katere odstranitev povzroči, da je dominantno število dobljenega grafa večje kot prej. Povezavno kritično število grafa je kardinalnost kritične množice povezav najmanjše moči. Označujemo ga z ?$b(G)$?, pomaga pa nam pri ocenjevanju občutljivosti povezovalnih omrežij na propad povezav. Povezavno kritično število krepkega produkta polnega grafa in poti je odvisno od velikosti polnega grafa ?$K_m$? in vrednosti ?$n$? po ?$\\pmod{3}$?. Za naravni števili ?$m$? in ?$n$?, ?$m\\geq 1$? in ?$n \\geq 2$?, velja, da je ?$b(K_m \\boxtimes P_n)=\\lceil \\frac{m}{2} \\rceil$?, če je ?$n\\equiv 0 \\pmod{3}$?, ?$b(K_m \\boxtimes P_n)=\\lceil \\frac{3m}{2} \\rceil$?, če je ?$n\\equiv 1 \\pmod{3}$? in ?$b(K_m \\boxtimes P_n)=m$?, če je ?$n\\equiv 2 \\pmod{3}$?"}],"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-4XHO3CGN","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-4XHO3CGN"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-4XHO3CGN/c8-c485ce4-4aea58e8-5a22d1cfbf1ae4e-/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:dataProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:doc-4XHO3CGN/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-4XHO3CGN"}}}}