A tree as a finite nonempty set with a binary operation

Nebeský, Ladislav. "A tree as a finite nonempty set with a binary operation." Mathematica Bohemica 125.4 (2000): 455-458. <http://eudml.org/doc/248678>.

@article{Nebeský2000,
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).},
author = {Nebeský, Ladislav},
journal = {Mathematica Bohemica},
keywords = {trees; geodetic graphs; binary operations; trees; geodetic graphs; binary operations},
language = {eng},
number = {4},
pages = {455-458},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A tree as a finite nonempty set with a binary operation},
url = {http://eudml.org/doc/248678},
volume = {125},
year = {2000},
}

TY - JOUR
AU - Nebeský, Ladislav
TI - A tree as a finite nonempty set with a binary operation
JO - Mathematica Bohemica
PY - 2000
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 125
IS - 4
SP - 455
EP - 458
AB - 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).
LA - eng
KW - trees; geodetic graphs; binary operations; trees; geodetic graphs; binary operations
UR - http://eudml.org/doc/248678
ER -