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Keywords:
trees; geodetic graphs; binary operations
trees; geodetic graphs; binary operations
Summary:
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).
References:
[1] G. Chartrand L. Lesniak: Graphs & Digraphs. Third edition. Chapman & Hall, London, 1996. MR 1408678
[2] L. Nebeský: An algebraic characterization of geodetic graphs. Czechoslovak Math. J. 48 (1998), 701-710. DOI 10.1023/A:1022435605919 | MR 1658245
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