{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,5,3]],"date-time":"2024-05-03T09:12:48Z","timestamp":1714727568976},"reference-count":23,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p> For a graph [Formula: see text], a Roman dominating function (RDF) [Formula: see text] has the property that every vertex [Formula: see text] with [Formula: see text] has a neighbor [Formula: see text] with [Formula: see text]. The weight of a RDF [Formula: see text] is the sum [Formula: see text], and the minimum weight of a RDF on [Formula: see text] is the Roman domination number [Formula: see text] of [Formula: see text]. The Roman bondage number [Formula: see text] of [Formula: see text] is the minimum cardinality of all sets [Formula: see text] for which [Formula: see text]. A graph [Formula: see text] is in the class [Formula: see text] if the Roman domination number remains unchanged when a vertex is deleted. In this paper, we obtain tight upper bounds for [Formula: see text] and [Formula: see text] provided a graph [Formula: see text] is in [Formula: see text]. We present necessary and sufficient conditions for a tree to be in the class [Formula: see text]. We give a constructive characterization of [Formula: see text]-trees using labelings. <\/jats:p>","DOI":"10.1142\/s179383091650049x","type":"journal-article","created":{"date-parts":[[2016,6,6]],"date-time":"2016-06-06T23:52:58Z","timestamp":1465257178000},"page":"1650049","source":"Crossref","is-referenced-by-count":6,"title":["Roman domination in graphs: The class \u211bUV R"],"prefix":"10.1142","volume":"08","author":[{"given":"Vladimir","family":"Samodivkin","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Architecture, Civil Engineering and Geodesy, Sofia 1046, Bulgaria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,8]]},"reference":[{"key":"S179383091650049XBIB001","doi-asserted-by":"publisher","DOI":"10.5711\/morj.1.3.3"},{"key":"S179383091650049XBIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830913500018"},{"key":"S179383091650049XBIB003","doi-asserted-by":"publisher","DOI":"10.2298\/AADM140210003B"},{"key":"S179383091650049XBIB004","doi-asserted-by":"publisher","DOI":"10.1137\/070699688"},{"key":"S179383091650049XBIB005","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830914500384"},{"key":"S179383091650049XBIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.004"},{"key":"S179383091650049XBIB007","first-page":"1487","volume":"5","author":"Ebadi K.","year":"2010","journal-title":"Int. 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