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MATHEMATICA BOHEMICA, Vol. 125, No. 4, pp. 455-458 (2000)
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# A tree as a finite nonempty set

with a binary operation

## Ladislav Nebesky

* Ladislav Nebesky*, Filozoficka fakulta Univerzity Karlovy, nam. J. Palacha 2, 116 38 Praha 1, Czech Republic, e-mail: ` ladislav.nebesky@ff.cuni.cz`

**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

**Full text of the article:**

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