Graham–Sloane harmonious labeling conjecture

Let $G$ be a graph with $m$ edges and at most $m$ vertices. A labeling $f:V(G)\to\mathbb{Z}_m$ is harmonious when the edge labels $f'(xy)=f(x)+f(y)$ are all distinct; for a tree on $n$ vertices, every label is required to be used on some vertex.

Graham–Sloane conjecture. Every tree is harmonious.

The source notes that almost all graphs are not harmonious, while a later theorem shows that every tree has an injective harmonious labeling using an Abelian group of order $n+o(n)$. The exact conjecture remains unresolved in the supplied text.