{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T09:11:17Z","timestamp":1777540277990,"version":"3.51.4"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p> A Roman dominating function (RDF) on a graph [Formula: see text] is a function [Formula: see text] satisfying the condition that every vertex [Formula: see text] for which [Formula: see text] is adjacent to at least one vertex [Formula: see text] for which [Formula: see text]. The weight of a RDF [Formula: see text] is the value [Formula: see text]. The Roman domination number, [Formula: see text], of [Formula: see text] is the minimum weight of a RDF on [Formula: see text]. An RDF [Formula: see text] is called an independent Roman dominating function (IRDF) if the set [Formula: see text] is an independent set. The independent Roman domination number, [Formula: see text], is the minimum weight of an IRDF on [Formula: see text]. In this paper, we study trees with independent Roman domination number twice their independent domination number, answering an open question. <\/jats:p>","DOI":"10.1142\/s1793830915500482","type":"journal-article","created":{"date-parts":[[2015,9,15]],"date-time":"2015-09-15T01:49:14Z","timestamp":1442281754000},"page":"1550048","source":"Crossref","is-referenced-by-count":8,"title":["Trees with independent Roman domination number twice the independent domination number"],"prefix":"10.1142","volume":"07","author":[{"given":"Mustapha","family":"Chellali","sequence":"first","affiliation":[{"name":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida. B. P. 270 Blida, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nader Jafari","family":"Rad","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Shahrood, Shahrood, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,1,4]]},"reference":[{"key":"S1793830915500482BIB001","first-page":"11","volume":"52","author":"Adabi M.","year":"2012","journal-title":"Aust. J. Comb."},{"key":"S1793830915500482BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.004"},{"key":"S1793830915500482BIB003","first-page":"673","volume":"32","author":"Chellali M.","year":"2012","journal-title":"Opuscula Math."},{"key":"S1793830915500482BIB004","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1669"},{"key":"S1793830915500482BIB005","first-page":"351","volume":"80","author":"Ebrahimi E.","year":"2012","journal-title":"J. Comb. Math. Comb. Comput."},{"key":"S1793830915500482BIB006","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S1793830915500482BIB007","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1178"},{"key":"S1793830915500482BIB008","first-page":"167","volume":"19","author":"Rad N. J.","year":"2011","journal-title":"Analele Stiintifice Universitatii Ovidius Constanta"},{"key":"S1793830915500482BIB010","first-page":"218","volume":"15","author":"Mojdeh D. A.","year":"2008","journal-title":"Scientia Iranica"},{"key":"S1793830915500482BIB011","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2000.12005243"},{"key":"S1793830915500482BIB012","doi-asserted-by":"publisher","DOI":"10.1038\/scientificamerican1299-136"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500482","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T16:34:00Z","timestamp":1565109240000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500482"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2016,1,4]]},"published-print":{"date-parts":[[2015,12]]}},"alternative-id":["10.1142\/S1793830915500482"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500482","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,12]]}}}