{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,6,22]],"date-time":"2023-06-22T10:50:42Z","timestamp":1687431042578},"reference-count":20,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,2]]},"abstract":"<jats:p> Let [Formula: see text] be a graph with vertex set [Formula: see text] and edge set [Formula: see text]. If [Formula: see text] has no isolated vertex, then a disjunctive total dominating set (DTD-set) of [Formula: see text] is a vertex set [Formula: see text] such that every vertex in [Formula: see text] is adjacent to a vertex of [Formula: see text] or has at least two vertices in [Formula: see text] at distance two from it, and the disjunctive total domination number [Formula: see text] of [Formula: see text] is the minimum cardinality overall DTD-sets of [Formula: see text]. Let [Formula: see text] and [Formula: see text] be two disjoint copies of a graph [Formula: see text], and let [Formula: see text] be a bijection. Then, a permutation graph [Formula: see text] has the vertex set [Formula: see text] and the edge set [Formula: see text]. For any connected graph [Formula: see text] of order at least three, we prove the sharp bounds [Formula: see text]; we give an example showing that [Formula: see text] can be arbitrarily large. We characterize permutation graphs for which [Formula: see text] holds. Further, we show that [Formula: see text] when [Formula: see text] is a cycle, a path, and a complete [Formula: see text]-partite graph, respectively. <\/jats:p>","DOI":"10.1142\/s1793830917500094","type":"journal-article","created":{"date-parts":[[2016,11,24]],"date-time":"2016-11-24T21:45:58Z","timestamp":1480023958000},"page":"1750009","source":"Crossref","is-referenced-by-count":2,"title":["Disjunctive total domination in permutation graphs"],"prefix":"10.1142","volume":"09","author":[{"given":"Eunjeong","family":"Yi","sequence":"first","affiliation":[{"name":"Texas A&amp;M University at Galveston, Galveston, TX 77553, USA"}]}],"member":"219","published-online":{"date-parts":[[2017,2,6]]},"reference":[{"key":"S1793830917500094BIB001","doi-asserted-by":"publisher","DOI":"10.1002\/net.20056"},{"key":"S1793830917500094BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.12.007"},{"key":"S1793830917500094BIB003","volume-title":"Theory of Graphs and its Applications","author":"Berge C.","year":"1962"},{"key":"S1793830917500094BIB004","volume-title":"Graphs and Hypergraphs","author":"Berge C.","year":"1973"},{"key":"S1793830917500094BIB005","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1233"},{"key":"S1793830917500094BIB006","first-page":"433","volume":"3","author":"Chartrand G.","year":"1967","journal-title":"Ann. 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