| Title:
|
Characterizing the interval function of a connected graph (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
123 |
| Issue:
|
2 |
| Year:
|
1998 |
| Pages:
|
137-144 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
As was shown in the book of Mulder [4], the interval function is an important tool for studying metric properties of connected graphs. An axiomatic characterization of the interval function of a connected graph was given by the present author in [5]. (Using the terminology of Bandelt, van de Vel and Verheul [1] and Bandelt and Chepoi [2], we may say that [5] gave a necessary and sufficient condition for a finite geometric interval space to be graphic).
In the present paper, the result given in [5] is extended. The proof is based on new ideas. (English) |
| Keyword:
|
graphs |
| Keyword:
|
distance |
| Keyword:
|
interval function |
| MSC:
|
05C12 |
| idZBL:
|
Zbl 0937.05036 |
| idMR:
|
MR1673965 |
| DOI:
|
10.21136/MB.1998.126307 |
| . |
| Date available:
|
2009-09-24T21:30:21Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126307 |
| . |
| Reference:
|
[1] H.-J. Bandelt M. van de Vel E.Verheul: Modular interval spaces.Math. Nachr. 163 (1993), 177-201. MR 1235066, 10.1002/mana.19931630117 |
| Reference:
|
[2] H.-J. Bandelt V. Chepoi: A Holly theorem in weakly modular space.Discrete Math. 160 (1996), 25-39. MR 1417558, 10.1016/0012-365X(95)00217-K |
| Reference:
|
[3] G. Chartrand L. Lesniak: Graphs & Digraphs.(third edition). Chapman & Hall, London, 1996. MR 1408678 |
| Reference:
|
[4] H. M. Mulder: The Interval Function of a Graph.Mathematisch Centrum, Amsterdam, 1980. Zbl 0446.05039, MR 0605838 |
| 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: Geodesics and steps in a connected graph.Czechoslovak Math. J. 47 (122) (1997), 149-161. MR 1435613, 10.1023/A:1022404624515 |
| Reference:
|
[7] E. R. Verheul: Multimedians in metric and normed spaces.CWI TRACT 91, Amsterdam, 1993. Zbl 0790.46008, MR 1244813 |
| . |
