{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:34:05Z","timestamp":1753882445559,"version":"3.41.2"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100006733","name":"Commission on Higher Education","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100006733","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> Let G be a connected graph. Brigham et al., Resolving domination in graphs, Math. Bohem. 1 (2003) 25\u201336 defined a resolving dominating set as a set S of vertices of a connected graph G that is both resolving and dominating. A resolving dominating is a 1-movable resolving dominating set of G if for every [Formula: see text], either [Formula: see text] is a resolving dominating set or there exists a vertex [Formula: see text] such that [Formula: see text] is a resolving dominating set of G. The minimum cardinality of a 1-movable resolving dominating set of G, denoted by [Formula: see text] is the 1-movable R-domination number of G. A 1-movable resolving dominating set with cardinality [Formula: see text] is called a [Formula: see text]-set of G. In this paper, we characterize the 1-movable resolving dominating sets in the join and lexicographic product of two graphs and determine the bounds or exact values of the 1-movable resolving domination number of these graphs. <\/jats:p>","DOI":"10.1142\/s1793830922500161","type":"journal-article","created":{"date-parts":[[2021,9,29]],"date-time":"2021-09-29T01:55:02Z","timestamp":1632880502000},"source":"Crossref","is-referenced-by-count":1,"title":["Movable resolving domination in graphs"],"prefix":"10.1142","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8888-5912","authenticated-orcid":false,"given":"Gerald B.","family":"Monsanto","sequence":"first","affiliation":[{"name":"College of Teacher Education, Arts and Sciences, Visayas State University-Villaba, Leyte 6537, Philippines"}]},{"given":"Helen M.","family":"Rara","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science and Mathematics, Center of Graph Theory, Algebra and Analysis-Premier Research Institute of Science and Mathematics Mindanao State University-Iligan, Institute of Technology, Iligan City 9200, Philippines"}]}],"member":"219","published-online":{"date-parts":[[2021,9,28]]},"reference":[{"volume-title":"Theorie des Graphes et Ses Applications","year":"1958","author":"Berge C.","key":"S1793830922500161BIB001"},{"key":"S1793830922500161BIB002","first-page":"102","volume":"77","author":"Blair J.","year":"2011","journal-title":"J. Comb. Math. Comb. Comput."},{"key":"S1793830922500161BIB003","doi-asserted-by":"publisher","DOI":"10.21136\/MB.2003.133935"},{"issue":"88","key":"S1793830922500161BIB004","first-page":"4381","volume":"8","author":"Canoy S.","year":"2014","journal-title":"Appl. Math. Sci."},{"key":"S1793830922500161BIB005","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100304"},{"key":"S1793830922500161BIB006","doi-asserted-by":"publisher","DOI":"10.21236\/AD0705364"},{"volume-title":"Fundamentals of Domination in Graphs","year":"1998","author":"Haynes T. W.","key":"S1793830922500161BIB007"},{"key":"S1793830922500161BIB008","doi-asserted-by":"publisher","DOI":"10.29020\/nybg.ejpam.v14i3.3985"},{"issue":"60","key":"S1793830922500161BIB009","first-page":"1129","volume":"9","author":"Omega S.","year":"2015","journal-title":"Appl. Math. Sci."},{"key":"S1793830922500161BIB010","doi-asserted-by":"publisher","DOI":"10.12988\/ijma.2016.511281"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830922500161","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T03:18:37Z","timestamp":1661483917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S1793830922500161"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,28]]},"references-count":10,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2022,8]]}},"alternative-id":["10.1142\/S1793830922500161"],"URL":"https:\/\/doi.org\/10.1142\/s1793830922500161","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2021,9,28]]},"article-number":"2250016"}}