| Title:
|
The interval function of a connected graph and a characterization of geodetic graphs (English) |
| Author:
|
Nebeský, Ladislav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
247-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The interval function (in the sense of H. M. Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebeský in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a characterization of geodetic graphs will be established; this characterization will utilize properties of the interval function. (English) |
| Keyword:
|
graphs |
| Keyword:
|
distance |
| Keyword:
|
interval function |
| Keyword:
|
geodetic graphs |
| MSC:
|
05C12 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 0977.05045 |
| idMR:
|
MR1826487 |
| DOI:
|
10.21136/MB.2001.133909 |
| . |
| Date available:
|
2009-09-24T21:49:48Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133909 |
| . |
| Reference:
|
[1] H.-J. Bandelt, H. M. Mulder: Regular pseudo-median graphs.J. Graph Theory 12 (1988), 533–549. MR 0968750, 10.1002/jgt.3190120410 |
| Reference:
|
[2] H.-J. Bandelt, H. M. Mulder: Three interval conditions for graphs.Ars Combin. 29B (1990), 213–223. MR 1412877 |
| Reference:
|
[3] H.-J. Bandelt, H. M. Mulder, E. Wilkeit: Quasi-median graphs and algebras.J. Graph Theory 18 (1994), 681–703. MR 1297190, 10.1002/jgt.3190180705 |
| Reference:
|
[4] H. M. Mulder: The Interval Function of a Graph.Mathematical Centre Tracts 132, Mathematisch Centrum, Amsterdam, 1980. Zbl 0446.05039, MR 0605838 |
| Reference:
|
[5] L. Nebeský: A characterization of the set of all shortest paths in a connected graph.Math. Bohem. 119 (1994), 15–20. MR 1303548 |
| Reference:
|
[6] L. Nebeský: A characterization of the interval function of a connected graph.Czechoslovak Math. J. 44 (1994), 173–178. MR 1257943 |
| Reference:
|
[7] L. Nebeský: A characterization of geodetic graphs.Czechoslovak Math. J. 45 (1995), 491–493. MR 1344515 |
| Reference:
|
[8] L. Nebeský: Characterizing the interval function of a connected graph.Math. Bohem. 123 (1998), 137–144. MR 1673965 |
| Reference:
|
[9] L. Nebeský: An algebraic characterization of geodetic graphs.Czechoslovak Math. J. 48 (1998), 701–710. MR 1658245, 10.1023/A:1022435605919 |
| Reference:
|
[10] O. Ore: Theory of Graphs.Amer. Math. Soc. Colloq. Publ. 38, Providence, R. I., 1962. Zbl 0105.35401, MR 0150753 |
| . |
