The augmented Zagreb index–atom-bond connectivity index extremal tree conjecture

Let $T$ be a tree on $n$ vertices. The augmented Zagreb index $AZI$ and the atom-bond connectivity index $ABC$ are graph invariants of $T$.

Extremal tree conjecture. The $n$-vertex tree $T$ has the maximum $AZI$ value if and only if $T$ has the minimum $ABC$ index.

This conjecture proposes that the trees maximizing the augmented Zagreb index are exactly the trees minimizing the atom-bond connectivity index. The source presents it as an open conjecture; no resolution is given there.