Kamatchi–Arumugam tree characterization conjecture for distance-antimagic trees

Let $T$ be a tree. A tree is distance antimagic if it admits a bijection $f:V(T)\to\{1,2,\ldots,|V(T)|\}$ whose vertex weights

$$w(v)=\sum_{u\in N(v)}f(u)$$

are distinct. A support vertex is a vertex adjacent to at least one leaf.

Kamatchi–Arumugam tree conjecture. $T$ is distance antimagic if and only if every support vertex $v$ has precisely one leaf adjacent to $v$.

The source explicitly describes this as one of the conjectures put forward by Kamatchi and Arumugam and says that these conjectures were yet open. It gives a proposed structural characterization of distance-antimagic trees.