Graham--Sloane harmonious tree conjecture

Let $T$ be a tree with $n$ vertices. A harmonious labelling assigns distinct vertex labels and gives an edge $uv$ the label $(\psi(u)+\psi(v))\bmod(n-1)$. Harmonious Tree Conjecture. For any $n$-vertex tree $T$ there exists an injective labelling

$$\psi:V(T) \rightarrow [n]$$

such that the values

$$\Big(\psi(u)+\psi(v)\mod (n-1)\Big)_{uv\in E(T)}$$

are pairwise distinct. This is the harmonious analogue of the graceful tree conjecture, introduced by Graham and Sloane; the source gives no resolution and the problem remains open.