On trees attaining an upper bound on the total domination number

‎A total dominating set of a graph G G is a set D D of vertices of G G such that every vertex of G G has a neighbor in D D ‎. ‎The total domination number of a graph G G ‎, ‎denoted by γ t (G) γt(G) ‎, ‎is~the minimum cardinality of a total dominating set of G G ‎. ‎Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004)‎, ‎69--75] established the following upper bound on the total domination number of a tree in terms of the order and the number of support vertices‎, ‎γ t (T)≤(n+s)/2 γt(T)≤(n+s)/2 ‎. ‎We characterize all trees attaining this upper bound‎.‎