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The eccentric distance sum of [Formula: see text] is defined as [Formula: see text], where [Formula: see text] is the maximum distance from [Formula: see text] to any other vertex and [Formula: see text] is the sum of all distances from [Formula: see text]. A set [Formula: see text] is a distance [Formula: see text]-dominating set of [Formula: see text] if for every vertex [Formula: see text], [Formula: see text] for some vertex [Formula: see text]. The minimum cardinality among all distance [Formula: see text]-dominating sets of [Formula: see text] is called the distance [Formula: see text]-domination number [Formula: see text] of [Formula: see text]. In this paper, the trees among all [Formula: see text]-vertex trees with distance [Formula: see text]-domination number [Formula: see text] having the minimal eccentric distance sum are determined. <\/jats:p>","DOI":"10.1142\/s1793830920500524","type":"journal-article","created":{"date-parts":[[2020,5,29]],"date-time":"2020-05-29T16:56:17Z","timestamp":1590771377000},"page":"2050052","source":"Crossref","is-referenced-by-count":4,"title":["The minimum eccentric distance sum of trees with given distance k-domination number"],"prefix":"10.1142","volume":"12","author":[{"given":"Lidan","family":"Pei","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Hefei Normal University, Hefei, Anhui, 230601, P. R. China"}]},{"given":"Xiangfeng","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, P. R. 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