trees; geodetic graphs; binary operations
A (finite) acyclic connected graph is called a tree. Let $W$ be a finite nonempty set, and let $ H(W)$ be the set of all trees $T$ with the property that $W$ is the vertex set of $T$. We will find a one-to-one correspondence between $ H(W)$ and the set of all binary operations on $W$ which satisfy a certain set of three axioms (stated in this note).
 G. Chartrand L. Lesniak: Graphs & Digraphs
. Third edition. Chapman & Hall, London, 1996. MR 1408678