{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T19:26:17Z","timestamp":1774466777578,"version":"3.50.1"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,4]]},"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] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] of [Formula: see text] for which [Formula: see text]. The weight of a RDF is the sum [Formula: see text], and the minimum weight of a RDF [Formula: see text] is the Roman domination number [Formula: see text]. A subset [Formula: see text] of [Formula: see text] is a [Formula: see text]-independent set of [Formula: see text] if every vertex of [Formula: see text] has at most one neighbor in [Formula: see text] The maximum cardinality of a [Formula: see text]-independent set of [Formula: see text] is the [Formula: see text]-independence number [Formula: see text] Both parameters are incomparable in general, however, we show that if [Formula: see text] is a tree, then [Formula: see text]. Moreover, all extremal trees attaining equality are characterized. <\/jats:p>","DOI":"10.1142\/s1793830917500239","type":"journal-article","created":{"date-parts":[[2017,2,10]],"date-time":"2017-02-10T00:55:11Z","timestamp":1486688111000},"page":"1750023","source":"Crossref","is-referenced-by-count":3,"title":["Roman domination and 2-independence in trees"],"prefix":"10.1142","volume":"09","author":[{"given":"Nac\u00e9ra","family":"Meddah","sequence":"first","affiliation":[{"name":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mustapha","family":"Chellali","sequence":"additional","affiliation":[{"name":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B.P. 270, Blida, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2017,4,13]]},"reference":[{"key":"S1793830917500239BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-011-1040-3"},{"key":"S1793830917500239BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.004"},{"key":"S1793830917500239BIB003","first-page":"301","volume-title":"Graph Theory with Applications to Algorithms and Computer Science","author":"Fink J. F.","year":"1985"},{"key":"S1793830917500239BIB004","first-page":"129","volume":"217","author":"Hedetniemi S. T.","year":"2013","journal-title":"Congr. Numer."},{"key":"S1793830917500239BIB005","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2000.12005243"},{"key":"S1793830917500239BIB006","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\/S1793830917500239","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T09:14:39Z","timestamp":1565169279000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500239"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4]]},"references-count":6,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2017,4,13]]},"published-print":{"date-parts":[[2017,4]]}},"alternative-id":["10.1142\/S1793830917500239"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500239","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4]]}}}