Conjecture that every nontrivial tree is harmonious

A graph $G$ is harmonious when it admits a harmonious labeling, namely an injective vertex labeling whose induced edge labels are also injective modulo $|E(G)|$; for trees, the definition allows at most one repeated vertex label. A tree is nontrivial if it has at least one edge. Harmonious-tree conjecture. Every nontrivial tree is harmonious. Many classes of trees are known to be harmonious, and super edge-magic trees are known to be harmonious, but the assertion for all trees remains open.