Abstract: 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).
Keywords: trees, geodetic graphs, binary operations
Classification (MSC2000): 05C05, 05C75, 20N02
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