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).
In [3], the present author used a binary operation as a tool for characterizing geodetic graphs. In this paper a new proof of the main result of the paper cited above is presented. The new proof is shorter and simpler.