{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T09:26:05Z","timestamp":1758273965029},"reference-count":17,"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":[[2017,10]]},"abstract":"<jats:p> In this paper, we consider dominating sets [Formula: see text] and [Formula: see text] such that [Formula: see text] and [Formula: see text] are disjoint and there exists a perfect matching between them. Let [Formula: see text] denote the cardinality of smallest such sets [Formula: see text] in [Formula: see text] (provided they exist, otherwise [Formula: see text]). This concept was introduced in [W. F. Klostermeyer, M. E. Messinger and A. Angeli Ayello, An eternal domination problem in grids, Theory Appl. Graphs 4(1) (2017) 23pp.] in the context of studying a certain graph protection problem. We characterize the trees [Formula: see text] for which [Formula: see text] equals a certain graph protection parameter and for which [Formula: see text], where [Formula: see text] is the independence number of [Formula: see text]. We also further study this parameter in graph products, e.g., by giving bounds for grid graphs, and in graphs of small independence number. <\/jats:p>","DOI":"10.1142\/s1793830917500653","type":"journal-article","created":{"date-parts":[[2017,9,7]],"date-time":"2017-09-07T22:38:03Z","timestamp":1504823883000},"page":"1750065","source":"Crossref","is-referenced-by-count":1,"title":["Disjoint dominating sets with a perfect matching"],"prefix":"10.1142","volume":"09","author":[{"given":"William F.","family":"Klostermeyer","sequence":"first","affiliation":[{"name":"School of Computing, University of North Florida, Jacksonville, FL 32224-2669, USA"}]},{"given":"Margaret-Ellen","family":"Messinger","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Mount Allison University, Sackville, NB, Canada"}]},{"given":"Alejandro Angeli","family":"Ayello","sequence":"additional","affiliation":[{"name":"Department of Combinatorics and Optimization, University of Waterloo, Waterloo, ON, Canada"}]}],"member":"219","published-online":{"date-parts":[[2017,11,2]]},"reference":[{"key":"S1793830917500653BIB001","doi-asserted-by":"publisher","DOI":"10.5711\/morj.1.3.3"},{"issue":"1","key":"S1793830917500653BIB002","first-page":"1","volume":"3","author":"Caro Y.","year":"2016","journal-title":"Theory Appl. 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