Independent domination in trees

Let G = (V,E) be a simple connected graph. A dominating set D subset of V is an independent dominating set of graph G if the subgraph induced by D is isomorphic to an empty graph. The minimum cardinality of an independent dominating set, denoted by i(G), is called the independent domination number of graph G. It is known that for any tree i(T) <= n(T)+gamma(T)+l(T)/4. The extremal trees attaining the bound is characterized, which answers the problem posed in [A. Cabrera-Mart & iacute;nez, New bounds on the double domination number of trees, Discrete Appl. Math. 315 (2022) 97-103].