| Title:
|
Domination in generalized Petersen graphs (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
11-16 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Generalized Petersen graphs are certain graphs consisting of one quadratic factor. For these graphs some numerical invariants concerning the domination are studied, namely the domatic number $d(G)$, the total domatic number $d_t(G)$ and the $k$-ply domatic number $d^k(G)$ for $k=2$ and $k=3$. Some exact values and some inequalities are stated. (English) |
| Keyword:
|
domatic number |
| Keyword:
|
total domatic number |
| Keyword:
|
$k$-ply domatic number |
| Keyword:
|
generalized Petersen graph |
| MSC:
|
05C38 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 0995.05107 |
| idMR:
|
MR1885452 |
| . |
| Date available:
|
2009-09-24T10:48:28Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127697 |
| . |
| Reference:
|
[1] C. Y. Chao and S. C. Han: A note on the toughness of generalized Petersen graphs.J. Math. Research & Exposition 12 (1987), 183–186. MR 1167349 |
| Reference:
|
[2] E. J. Cockayne and S. T. Hedetniemi: Towards the theory of domination in graphs.Networks 7 (1977), 247–261. MR 0483788, 10.1002/net.3230070305 |
| Reference:
|
[3] E. J. Cockayne, S. T. Hedetniemi and R. M. Dawes: Total domination in graphs.Networks 10 (1980), 211–219. MR 0584887, 10.1002/net.3230100304 |
| Reference:
|
[4] W. Dörfler: On mapping graphs and permutation graphs.Math. Slovaca (1979), 215–228. |
| Reference:
|
[5] B. Piazza, R. Ringeisen and S. Stueckle: On the vulnerability of cycle permutation graphs.Ars Combinatoria 29 (1990), 289–296. MR 1046114 |
| Reference:
|
[6] B. Zelinka: On $k$-ply domatic numbers of graphs.Math. Slovaca 34 (1985), 313–318. MR 0756989 |
| . |
