Geodesic
A tree as a finite nonempty set with a binary operation
Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 455-458.

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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).
DOI : 10.21136/MB.2000.126275
Classification : 05C05, 05C75, 20N02
Keywords: trees; geodetic graphs; binary operations 
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Nebeský, Ladislav. A tree as a finite nonempty set with a binary operation. Mathematica Bohemica, Tome 125 (2000) no. 4, pp. 455-458. doi : 10.21136/MB.2000.126275. http://geodesic.mathdoc.fr/articles/10.21136/MB.2000.126275/

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