Characterization of trees attaining the independent locating-dominating bound

Let $T$ be a tree, let $(T)$ denote its independent locating-dominating number, and let $_{l}(T)$ denote its locating-dominating number.

Characterization problem. Characterize those trees $T$ for which

$$\iota(T)=\gamma_{l}(T).$$

The paper identifies this as an open problem arising from its bounds for independent locating-dominating sets in trees; a characterization of all equality cases remains to be found.