{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T08:25:58Z","timestamp":1649060758151},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,10]]},"abstract":"<jats:p> A Roman dominating function of a graph [Formula: see text] is a labeling [Formula: see text] such that every vertex with label [Formula: see text] has a neighbor with label [Formula: see text]. The Roman domination number, [Formula: see text] of [Formula: see text], is the minimum of [Formula: see text] over such functions. Let [Formula: see text] be an [Formula: see text]-vertex graph. Chambers et al. [E. W. Chambers, B. Kinnersley, N. Prince and D. B. West, External Problems for Roman domination Siam J. Discrete Math.\u00a023 (2009) 1575\u20131586.] proved that if [Formula: see text] is a connected graph of order [Formula: see text], then [Formula: see text], with equality if and only if [Formula: see text] or [Formula: see text] is [Formula: see text] or [Formula: see text]. In this paper, we construct a specific family of graphs [Formula: see text], and prove that if [Formula: see text] and [Formula: see text], then [Formula: see text], and this bound is sharp. <\/jats:p>","DOI":"10.1142\/s1793830919500551","type":"journal-article","created":{"date-parts":[[2019,8,21]],"date-time":"2019-08-21T02:40:48Z","timestamp":1566355248000},"page":"1950055","source":"Crossref","is-referenced-by-count":2,"title":["A Nordhaus\u2013Gaddum bound for Roman domination"],"prefix":"10.1142","volume":"11","author":[{"given":"Nader Jafari","family":"Rad","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shahed University, Tehran, Iran"}]},{"given":"Hadi","family":"Rahbani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shahrood University of Technology, Shahrood, Iran"}]}],"member":"219","published-online":{"date-parts":[[2019,11,3]]},"reference":[{"key":"S1793830919500551BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2016.03.017"},{"key":"S1793830919500551BIB002","doi-asserted-by":"publisher","DOI":"10.2298\/AADM140210003B"},{"key":"S1793830919500551BIB003","doi-asserted-by":"publisher","DOI":"10.1137\/070699688"},{"key":"S1793830919500551BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-015-1566-x"},{"key":"S1793830919500551BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2015.11.013"},{"key":"S1793830919500551BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2003.06.004"},{"key":"S1793830919500551BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(02)00811-7"},{"key":"S1793830919500551BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-012-9482-y"},{"key":"S1793830919500551BIB009","doi-asserted-by":"publisher","DOI":"10.2307\/2306658"},{"key":"S1793830919500551BIB010","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.2000.12005243"},{"key":"S1793830919500551BIB011","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\/S1793830919500551","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T06:14:51Z","timestamp":1572848091000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500551"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10]]},"references-count":11,"journal-issue":{"issue":"05","published-print":{"date-parts":[[2019,10]]}},"alternative-id":["10.1142\/S1793830919500551"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500551","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10]]}}}