| Title:
|
A characterization of the interval function of a (finite or infinite) connected graph (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
635-642 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
By the interval function of a finite connected graph we mean the interval function in the sense of H. M. Mulder. This function is very important for studying properties of a finite connected graph which depend on the distance between vertices. The interval function of a finite connected graph was characterized by the present author. The interval function of an infinite connected graph can be defined similarly to that of a finite one. In the present paper we give a characterization of the interval function of each connected graph. (English) |
| Keyword:
|
distance in a graph |
| Keyword:
|
interval function |
| MSC:
|
05C12 |
| idZBL:
|
Zbl 1079.05505 |
| idMR:
|
MR1851552 |
| . |
| Date available:
|
2009-09-24T10:45:49Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127674 |
| . |
| Reference:
|
[1] H.-J. Bandelt and V. Chepoi: A Helly theorem in weakly modular space.Discrete Math. 160 (1996), 25–39. MR 1417558, 10.1016/0012-365X(95)00217-K |
| Reference:
|
[2] H.-J. Bandelt, M. van de Vel and E. Verheul: Modular interval spaces.Math. Nachr. 163 (1993), 177–201. MR 1235066, 10.1002/mana.19931630117 |
| Reference:
|
[3] H. M. Mulder: The Interval Function of a Graph.Mathematish Centrum, Amsterdam, 1980. Zbl 0446.05039, MR 0605838 |
| Reference:
|
[4] H. M. Mulder: Transit functions on graphs.In preparation. Zbl 1166.05019 |
| Reference:
|
[5] L. Nebeský: A characterization of the interval function of a connected graph.Czechoslovak Math. J. 44(119) (1994), 173–178. MR 1257943 |
| Reference:
|
[6] L. Nebeský: Characterizing the interval function of a connected graph.Math. Bohem. 123 (1998), 137–144. MR 1673965 |
| . |
