Previous |  Up |  Next


trees; geodetic graphs; binary operations
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).
[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
Partner of
EuDML logo