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Res."],"accepted":{"date-parts":[[2022,5,26]]},"published-print":{"date-parts":[[2022,7]]},"abstract":"<jats:p>For a graph <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic>,\u00a0<jats:italic>E<\/jats:italic>), a restrained double Roman dominating function is a function <jats:italic>f<\/jats:italic> : <jats:italic>V<\/jats:italic>\u00a0\u2192\u00a0{0,\u00a01,\u00a02,\u00a03} having the property that if <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>) = 0, then the vertex <jats:italic>v<\/jats:italic> must have at least two neighbors assigned 2 under <jats:italic>f<\/jats:italic> or one neighbor <jats:italic>w<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>w<\/jats:italic>) = 3, and if <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>) = 1, then the vertex <jats:italic>v<\/jats:italic> must have at least one neighbor <jats:italic>w<\/jats:italic> with <jats:italic>f<\/jats:italic>(<jats:italic>w<\/jats:italic>)\u00a0\u2265\u00a02, and at the same time, the subgraph <jats:italic>G<\/jats:italic>[<jats:italic>V<\/jats:italic>0] which includes vertices with zero labels has no isolated vertex. The weight of a restrained double Roman dominating function <jats:italic>f<\/jats:italic> is the sum <jats:italic>f<\/jats:italic>(<jats:italic>V<\/jats:italic>)\u00a0=\u00a0\u2211<jats:sub><jats:italic>v<\/jats:italic>\u2208<jats:italic>V<\/jats:italic>\u00a0<\/jats:sub><jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>), and the minimum weight of a restrained double Roman dominating function on <jats:italic>G<\/jats:italic> is the restrained double Roman domination number of <jats:italic>G<\/jats:italic>. We initiate the study of restrained double Roman domination with proving that the problem of computing this parameter is <jats:italic>NP<\/jats:italic>-hard. Then we present an upper bound on the restrained double Roman domination number of a connected graph <jats:italic>G<\/jats:italic> in terms of the order of <jats:italic>G<\/jats:italic> and characterize the graphs attaining this bound. We study the restrained double Roman domination <jats:italic>versus<\/jats:italic> the restrained Roman domination. Finally, we investigate the bounds for the restrained double Roman domination of trees and determine trees <jats:italic>T<\/jats:italic> attaining the exhibited bounds.<\/jats:p>","DOI":"10.1051\/ro\/2022089","type":"journal-article","created":{"date-parts":[[2022,5,31]],"date-time":"2022-05-31T18:50:31Z","timestamp":1654023031000},"page":"2293-2304","source":"Crossref","is-referenced-by-count":9,"title":["Restrained double Roman domination of a graph"],"prefix":"10.1051","volume":"56","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9373-3390","authenticated-orcid":false,"given":"Doost Ali","family":"Mojdeh","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5215-615X","authenticated-orcid":false,"given":"Iman","family":"Masoumi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lutz","family":"Volkmann","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2022,7,29]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1016\/j.dam.2018.03.026","volume":"244","author":"Anu","year":"2018","journal-title":"Discret. 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