A tree as a finite nonempty set with a binary operation

Ladislav Nebeský

Mathematica Bohemica (2000)

  • Volume: 125, Issue: 4, page 455-458
  • ISSN: 0862-7959

Abstract

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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).

How to cite

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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 -

Citations in EuDML Documents

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  1. Ladislav Nebeský, New proof of a characterization of geodetic graphs
  2. Ladislav Nebeský, Travel groupoids
  3. Henry Martyn Mulder, Ladislav Nebeský, Leaps: an approach to the block structure of a graph
  4. Henry Martyn Mulder, Ladislav Nebeský, Modular and median signpost systems and their underlying graphs
  5. Ladislav Nebeský, Signpost systems and spanning trees of graphs
  6. Ladislav Nebeský, On properties of a graph that depend on its distance function
  7. Jung Rae Cho, Jeongmi Park, Yoshio Sano, Travel groupoids on infinite graphs

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