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Res."],"accepted":{"date-parts":[[2023,2,10]]},"published-print":{"date-parts":[[2023,3]]},"abstract":"<jats:p>An independent Roman dominating function (IRD-function) on a graph <jats:italic>G<\/jats:italic> is a function <jats:italic>f<\/jats:italic>\u00a0:\u00a0<jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>)\u00a0\u2192\u00a0{0,\u00a01,\u00a02} satisfying the conditions that (i) every vertex <jats:italic>u<\/jats:italic> for which <jats:italic>f<\/jats:italic>(<jats:italic>u<\/jats:italic>)\u00a0=\u00a00 is adjacent to at least one vertex <jats:italic>v<\/jats:italic> for which <jats:italic>f<\/jats:italic>(<jats:italic>v<\/jats:italic>)\u00a0=\u00a02, and (ii) the set of all vertices assigned non-zero values under <jats:italic>f<\/jats:italic> is independent. The weight of an IRD-function is the sum of its function values over all vertices, and the independent Roman domination number <jats:italic>i<\/jats:italic><jats:sub>R<\/jats:sub>(<jats:italic>G<\/jats:italic>) of <jats:italic>G<\/jats:italic> is the minimum weight of an IRD-function on <jats:italic>G<\/jats:italic>. In this paper, we initiate the study of the independent Roman bondage number <jats:italic>b<\/jats:italic><jats:sub><jats:italic>iR<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) of a graph <jats:italic>G<\/jats:italic> having at least one component of order at least three, defined as the smallest size of set of edges <jats:italic>F<\/jats:italic>\u00a0\u2286\u00a0<jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>) for which <jats:italic>i<\/jats:italic><jats:sub><jats:italic>R<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>\u00a0\u2212\u00a0<jats:italic>F<\/jats:italic>)\u00a0&gt;\u00a0<jats:italic>i<\/jats:italic><jats:sub><jats:italic>R<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>). We begin by showing that the decision problem associated with the independent Roman bondage problem is NP-hard for bipartite graphs. Then various upper bounds on <jats:italic>b<\/jats:italic><jats:sub><jats:italic>iR<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) are established as well as exact values on it for some special graphs. In particular, for trees <jats:italic>T<\/jats:italic> of order at least three, it is shown that <jats:italic>b<\/jats:italic><jats:sub><jats:italic>iR<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>)\u00a0\u2264\u00a03, while for connected planar graphs the upper bounds are in terms of the maximum degree with refinements depending on the girth of the graph.<\/jats:p>","DOI":"10.1051\/ro\/2023017","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T19:58:34Z","timestamp":1676318314000},"page":"371-382","source":"Crossref","is-referenced-by-count":2,"title":["Independent Roman bondage of graphs"],"prefix":"10.1051","volume":"57","author":[{"given":"Saeed","family":"Kosari","sequence":"first","affiliation":[]},{"given":"Jafar","family":"Amjadi","sequence":"additional","affiliation":[]},{"given":"Mustapha","family":"Chellali","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2298-4744","authenticated-orcid":false,"given":"Seyed Mahmoud","family":"Sheikholeslami","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2023,3,15]]},"reference":[{"key":"R1","first-page":"11","volume":"52","author":"Adabi","year":"2012","journal-title":"Australas. 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