| Title:
|
An algebraic characterization of geodetic graphs (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
701-710 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We say that a binary operation $*$ is associated with a (finite undirected) graph $G$ (without loops and multiple edges) if $*$ is defined on $V(G)$ and $uv\in E(G)$ if and only if $u\ne v$, $u * v=v$ and $v*u=u$ for any $u$, $v\in V(G)$. In the paper it is proved that a connected graph $G$ is geodetic if and only if there exists a binary operation associated with $G$ which fulfils a certain set of four axioms. (This characterization is obtained as an immediate consequence of a stronger result proved in the paper). (English) |
| MSC:
|
05C12 |
| MSC:
|
05C38 |
| MSC:
|
05C75 |
| MSC:
|
20N02 |
| idZBL:
|
Zbl 0949.05022 |
| idMR:
|
MR1658245 |
| . |
| Date available:
|
2009-09-24T10:17:29Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127448 |
| . |
| Reference:
|
[1] M. Behzad, G. Chartrand and L. Lesniak-Foster: Graphs & Digraphs.Prindle, Weber & Schmidt, Boston, 1979. MR 0525578 |
| Reference:
|
[2] F. Harary: Graph Theory.Addison-Wesley, Reading (Mass.), 1969. Zbl 0196.27202, MR 0256911 |
| Reference:
|
[3] H. M. Mulder: The Interval Function of a Graph.Mathematisch Centrum. Amsterdam, 1980. Zbl 0446.05039, MR 0605838 |
| Reference:
|
[4] L. Nebeský: A characterization of the set of all shortest paths in a connected graph.Mathematica Bohemica 119 (1994), 15–20. MR 1303548 |
| Reference:
|
[5] L. Nebeský: A characterization of geodetic graphs.Czechoslovak Math. Journal 45 (120) (1995), 491–493. MR 1344515 |
| Reference:
|
[6] L. Nebeský: Geodesics and steps in a connected graph.Czechoslovak Math. Journal 47 (122) (1997), 149–161. MR 1435613, 10.1023/A:1022404624515 |
| . |
