| Title:
|
Spherical and clockwise spherical graphs
(English)
|
| Author:
|
Berrachedi, Abdelhafid |
| Author:
|
Havel, Ivan |
| Author:
|
Mulder, Henry Martyn |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 |
| Volume:
|
53 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
295-309 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main subject of our study are spherical (weakly spherical) graphs, i.e. connected graphs fulfilling the condition that in each interval to each vertex there is exactly one (at least one, respectively) antipodal vertex. Our analysis concerns properties of these graphs especially in connection with convexity and also with hypercube graphs. We deal e.g. with the problem under what conditions all intervals of a spherical graph induce hypercubes and find a new characterization of hypercubes: $G$ is a hypercube if and only if $G$ is spherical and bipartite. |
| Keyword:
|
spherical graph |
| Keyword:
|
hypercube |
| Keyword:
|
antipodal vertex |
| Keyword:
|
interval |
| MSC:
|
05C12 |
| MSC:
|
05C65 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 1021.05085 |
| idMR:
|
MR1983453 |
| . |
| Date available:
|
2009-09-24T11:01:44Z |
| Last updated:
|
2012-05-31 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127801 |
| . |
| Reference:
|
[1] A. Berman and A. Kotzig: Cross-cloning and antipodal graphs.Discrete Math. 69 (1988), 107–114. MR 0937775 |
| Reference:
|
[2] S. L. Bezrukov: Private communication.. |
| Reference:
|
[3] A. E. Brouwer, A. M. Cohen and A. Neumaier: Distance-regular graphs. A Series of Modern Surveys in Mathematics.Springer Verlag, Berlin-Heidelberg-New York, 1989. MR 1002568 |
| Reference:
|
[4] G. Burosch: Hasse Graphen spezieller Ordnungen.In: K. Wagner, R. Bodendiek: Graphentheorie I. Anwendungen auf Topologie, Gruppentheorie und Verbandstheorie, B. I, Wissenschaftsverlag, Mannheim-Wien-Zurich, 1989, pp. 157–235. |
| Reference:
|
[5] G. Burosch, I. Havel and J.-M. Laborde: Distance monotone graphs and a new characterization of hypercubes.Discrete Math. 110 (1992), 9–16. MR 1197441 |
| Reference:
|
[6] F. Harary: Four difficult unsolved problems in graph theory.Recent Advances in Graph Theory, M. Fiedler (ed.), Academia, Praha, 1974, pp. 249–256. MR 0382042 |
| Reference:
|
[7] M. Mollard: Interval-regularity does not lead to interval monotonicity.Discrete Math. 118 (1993), 233–237. Zbl 0784.05040, MR 1230065 |
| Reference:
|
[8] H. M. Mulder: The interval function of a graph.Mathematical Centre Tracts 132, Mathematisch Centrum Amsterdam, 1980. Zbl 0446.05039, MR 0605838 |
| Reference:
|
[9] H. M. Mulder: Interval-regular graphs.Discrete Math. 44 (1982), 253–269. Zbl 0542.05051, MR 0676887 |
| Reference:
|
[10] K. Nomura: Private communication.. |
| . |
