{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,11]],"date-time":"2026-04-11T07:42:57Z","timestamp":1775893377198,"version":"3.50.1"},"reference-count":12,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,4]]},"abstract":"<jats:p> A double Roman dominating function (DRDF) on a graph [Formula: see text] is a function [Formula: see text] such that (i) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least two vertices assigned a [Formula: see text] or to at least one vertex assigned a [Formula: see text] and (ii) every vertex [Formula: see text] with [Formula: see text] is adjacent to at least one vertex [Formula: see text] with [Formula: see text] The weight of a DRDF is the sum of its function values over all vertices. The double Roman domination number [Formula: see text] equals the minimum weight of a DRDF on [Formula: see text] The concept of criticality with respect to various operations on graphs has been studied for several domination parameters. In this paper, we study the concept of criticality for double Roman domination in graphs. In addition, we characterize double Roman domination edge super critical graphs and we will give several characterizations for double Roman domination vertex (edge) critical graphs. <\/jats:p>","DOI":"10.1142\/s1793830920500202","type":"journal-article","created":{"date-parts":[[2019,12,9]],"date-time":"2019-12-09T06:09:13Z","timestamp":1575871753000},"page":"2050020","source":"Crossref","is-referenced-by-count":13,"title":["Critical concept for double Roman domination in graphs"],"prefix":"10.1142","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4955-7227","authenticated-orcid":false,"given":"S.","family":"Nazari-Moghaddam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dehloran Branch University of Applied, Science and Technology, Dehloran, Iran"}]},{"given":"L.","family":"Volkmann","sequence":"additional","affiliation":[{"name":"Lehrstuhl II f\u00fcr Mathematik, RWTH Aachen University, 52056 Aachen, Germany"}]}],"member":"219","published-online":{"date-parts":[[2020,2,28]]},"reference":[{"key":"S1793830920500202BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s40995-018-0535-7"},{"key":"S1793830920500202BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2017.06.014"},{"key":"S1793830920500202BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-018-0286-6"},{"key":"S1793830920500202BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2018.03.026"},{"key":"S1793830920500202BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2016.03.017"},{"key":"S1793830920500202BIB008","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S1793830920500202BIB009","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"S1793830920500202BIB010","first-page":"79","volume":"89","author":"Rad N. Jafari","year":"2012","journal-title":"Util. Math."},{"key":"S1793830920500202BIB011","first-page":"205","volume":"104","author":"Volkmann L.","year":"2018","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"S1793830920500202BIB012","first-page":"71","volume":"3","author":"Volkmann L.","year":"2018","journal-title":"Commun. Comb. Optim."},{"key":"S1793830920500202BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2018.06.033"},{"key":"S1793830920500202BIB014","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2018.01.004"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500202","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,18]],"date-time":"2020-05-18T05:59:31Z","timestamp":1589781571000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,28]]},"references-count":12,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2020,4]]}},"alternative-id":["10.1142\/S1793830920500202"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500202","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,28]]}}}