{"?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-K5V48XH8/91c87a26-8a40-4253-ae4c-391992b99137/PDF","dcterms:extent":"252 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:doc-K5V48XH8/1217fe04-5a68-4a7e-9d5a-67d43199120b/TEXT","dcterms:extent":"27 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-K5V48XH8","dcterms:isPartOf":[{"@rdf:resource":"https://www.dlib.si/details/URN:NBN:SI:spr-UP1WMFAR"},{"@xml:lang":"sl","#text":"Ars mathematica contemporanea"}],"dcterms:issued":"2020","dc:creator":["Klobučar, Ana","Klobučar, Antoaneta"],"dc:format":[{"@xml:lang":"sl","#text":"letnik:19"},{"@xml:lang":"sl","#text":"številka:2"},{"@xml:lang":"sl","#text":"str. 337-349"}],"dc:identifier":["ISSN:1855-3974","COBISSID_HOST:44983555","URN:URN:NBN:SI:doc-K5V48XH8"],"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":"cardinal products of graphs"},{"@xml:lang":"sl","#text":"cikli"},{"@xml:lang":"en","#text":"cycles"},{"@xml:lang":"en","#text":"double Roman domination"},{"@xml:lang":"sl","#text":"dvojna rimljanska dominacija"},{"@xml:lang":"sl","#text":"kardinalni produkti grafov"},{"@xml:lang":"en","#text":"paths"},{"@xml:lang":"sl","#text":"poti"},{"@xml:lang":"sl","#text":"rimljanska dominacija"},{"@xml:lang":"en","#text":"Roman domination"}],"dcterms:temporal":{"@rdf:resource":"2008-2025"},"dc:title":{"@xml:lang":"sl","#text":"Properties of double Roman domination on cardinal products of graphs|"},"dc:description":[{"@xml:lang":"sl","#text":"Double Roman domination is a stronger version of Roman domination that doubles the protection. The areas now have 0, 1, 2 or 3 legions. Every attacked area needs 2 legions for its defence, either their own, or borrowed from 1 or 2 neighbouring areas, which still have to keep at least 1 legion to themselves. The minimal number of legions in all areas together is equal to the double Roman domination number. In this paper we determine an upper bound and a lower bound for double Roman domination numbers on cardinal product of any two graphs. Also we determine the exact values of double Roman domination numbers on ?$P_2 \\times G$? (for many types of graph ?$G$?). Also, the double Roman domination number is found for ?$P_2 \\times P_n$?, ?$P_3 \\times P_n$?, ?$P_4 \\times P_n$?, while upper and lower bounds are given for ?$P_5 \\times P_n$? and ?$P_6 \\times P_n$?. Finally, we will give a case study to determine the efficiency of double protection. We will compare double Roman domination versus Roman domination by running a simulation of a battle"},{"@xml:lang":"sl","#text":"Dvojna rimljanska dominacija je krepkejša verzija rimljanske dominacije, ki podvaja zaščito. Območja imajo zdaj 0, 1, 2 ali 3 legije. Vsako napadeno območje potrebuje 2 legiji za svojo obrambo, in to bodisi lastni bodisi izposojeni od 1 ali 2 sosednih območij, ki pa morata še vedno ohraniti najmanj 1 legijo zase. Minimalno število legij na vseh območjih skupaj je enako dvojnemu rimljanskemu dominacijskemu številu. V tem članku določimo zgornjo mejo in spodnjo mejo za dvojno rimljansko dominacijska števila kardinalnih produktov poljubnih dveh grafov. Prav tako določimo natančne vrednosti dvojno rimljanskih dominacijskih števil grafov ?$P_2 \\times G$? (za mnoge vrste grafa ?$G$?). Prav tako najdemo dvojno rimljansko dominacijsko število grafov ?$P_2 \\times P_n$?, ?$P_3 \\times P_n$?, ?$P_4 \\times P_n$?, za grafa ?$P_5 \\times P_n$? in ?$P_6 \\times P_n$? pa predstavimo zgornji in spodnji meji. Nazadnje predstavimo študijo primera za določitev učinkovitosti dvojne zaščite. Primerjali bomo dvojno rimljansko dominacijo in rimljansko dominacijo na ta način, da bomo pognali simulacijo bitke"}],"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-K5V48XH8","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:doc-K5V48XH8"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:doc-K5V48XH8/91c87a26-8a40-4253-ae4c-391992b99137/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-K5V48XH8/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:doc-K5V48XH8"}}}}