| Title:
|
A tree as a finite nonempty set with a binary operation (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
125 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
455-458 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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). (English) |
| Keyword:
|
trees |
| Keyword:
|
geodetic graphs |
| Keyword:
|
binary operations |
| MSC:
|
05C05 |
| MSC:
|
05C75 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 0963.05032 |
| idMR:
|
MR1802293 |
| DOI:
|
10.21136/MB.2000.126275 |
| . |
| Date available:
|
2009-09-24T21:45:28Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126275 |
| . |
| Reference:
|
[1] G. Chartrand L. Lesniak: Graphs & Digraphs.Third edition. Chapman & Hall, London, 1996. MR 1408678 |
| Reference:
|
[2] L. Nebeský: An algebraic characterization of geodetic graphs.Czechoslovak Math. J. 48 (1998), 701-710. MR 1658245, 10.1023/A:1022435605919 |
| . |
