# A tree as a finite nonempty set with a binary operation

Mathematica Bohemica (2000)

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

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topNebeský, 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 -

## References

top- G. Chartrand L. Lesniak, Graphs & Digraphs, Third edition. Chapman & Hall, London, 1996. (1996) MR1408678
- L. Nebeský, 10.1023/A:1022435605919, Czechoslovak Math. J. 48 (1998), 701-710. (1998) MR1658245DOI10.1023/A:1022435605919

## Citations in EuDML Documents

top- Ladislav Nebeský, New proof of a characterization of geodetic graphs
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- Henry Martyn Mulder, Ladislav Nebeský, Modular and median signpost systems and their underlying graphs
- Jung Rae Cho, Jeongmi Park, Yoshio Sano, Travel groupoids on infinite graphs
- Ladislav Nebeský, On properties of a graph that depend on its distance function
- Ladislav Nebeský, Signpost systems and spanning trees of graphs

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