{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,14]],"date-time":"2025-05-14T02:30:04Z","timestamp":1747189804547,"version":"3.40.5"},"reference-count":20,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,6]]},"abstract":"<jats:p> Let [Formula: see text] be a positive integer and [Formula: see text] be a simple graph. A restrained[Formula: see text]-rainbow dominating function (R[Formula: see text]RDF) of [Formula: see text] is a function [Formula: see text] from the vertex set [Formula: see text] to the family of all subsets of [Formula: see text], such that every vertex [Formula: see text] with [Formula: see text] satisfies both of the conditions [Formula: see text] and [Formula: see text] simultaneously, where [Formula: see text] denotes the open neighborhood of [Formula: see text]. The weight of an R[Formula: see text]RDF is the value [Formula: see text]. The restrained[Formula: see text]-rainbow domination number of [Formula: see text], denoted by [Formula: see text], is the minimum weight of an R[Formula: see text]RDF of [Formula: see text]. The restrained[Formula: see text]-rainbow reinforcement number [Formula: see text] of [Formula: see text], is defined to be the minimum number of edges that must be added to [Formula: see text] in order to decrease the restrained [Formula: see text]-rainbow domination number. In this paper, we determine the restrained [Formula: see text]-rainbow reinforcement number of some special classes of graphs. Also, we present some bounds on the restrained [Formula: see text]-rainbow reinforcement number of general graphs. <\/jats:p>","DOI":"10.1142\/s1793830921500269","type":"journal-article","created":{"date-parts":[[2020,9,19]],"date-time":"2020-09-19T04:08:30Z","timestamp":1600488510000},"page":"2150026","source":"Crossref","is-referenced-by-count":3,"title":["The restrained k-rainbow reinforcement number of graphs"],"prefix":"10.1142","volume":"13","author":[{"given":"Saeed","family":"Shaebani","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Damghan University, 36716\u201341167, Damghan, Iran"}]},{"given":"Saeed","family":"Kosari","sequence":"additional","affiliation":[{"name":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou, P. R. 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