| Title:
|
On the distance function of a connected graph (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1101-1106 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
An axiomatic characterization of the distance function of a connected graph is given in this note. The triangle inequality is not contained in this characterization. (English) |
| Keyword:
|
connected graph |
| Keyword:
|
distance function |
| MSC:
|
05C12 |
| MSC:
|
05C40 |
| idZBL:
|
Zbl 1174.05039 |
| idMR:
|
MR2471169 |
| . |
| Date available:
|
2010-07-21T08:11:46Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140443 |
| . |
| Reference:
|
[1] Kay, D. C., Chartrand, G.: A characterization of certain ptolemaic graphs.Canad. J. Math. 17 (1965), 342-346. Zbl 0139.17301, MR 0175113, 10.4153/CJM-1965-034-0 |
| Reference:
|
[2] Mulder, H. M.: The interval function of a graph.Math. Centre Tracts 132, Math. Centre, Amsterdam (1980). Zbl 0446.05039, MR 0605838 |
| Reference:
|
[3] Nebeský, L.: A characterization of the set of all shortest paths in a connected graph.Math. Bohem. 119 (1994), 15-20. MR 1303548 |
| Reference:
|
[4] Nebeský, L.: A characterization of the interval function of a connected graph.Czech. Math. J. 44 (1994), 173-178. MR 1257943 |
| Reference:
|
[5] Nebeský, L.: Geodesics and steps in a connected graph.Czech. Math. J. 47 (1997), 149-161. MR 1435613, 10.1023/A:1022404624515 |
| Reference:
|
[6] Nebeský, L.: A characterization of the interval function of a (finite or infinite) connected graph.Czech. Math. J. 51 (2001), 635-642. Zbl 1079.05505, MR 1851552, 10.1023/A:1013744324808 |
| . |
