| Title:
|
Remarks on restrained domination and total restrained domination in graphs (English) |
| Author:
|
Zelinka, Bohdan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
55 |
| Issue:
|
2 |
| Year:
|
2005 |
| Pages:
|
393-396 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The restrained domination number $\gamma ^r (G)$ and the total restrained domination number $\gamma ^r_t (G)$ of a graph $G$ were introduced recently by various authors as certain variants of the domination number $\gamma (G)$ of $(G)$. A well-known numerical invariant of a graph is the domatic number $d (G)$ which is in a certain way related (and may be called dual) to $\gamma (G)$. The paper tries to define analogous concepts also for the restrained domination and the total restrained domination and discusses the sense of such new definitions. (English) |
| Keyword:
|
domination number |
| Keyword:
|
domatic number |
| Keyword:
|
total domination number |
| Keyword:
|
total domatic number |
| Keyword:
|
restrained domination number |
| Keyword:
|
restrained domatic number |
| Keyword:
|
total restrained domination number |
| Keyword:
|
total restrained domatic number |
| MSC:
|
05C35 |
| MSC:
|
05C69 |
| idZBL:
|
Zbl 1081.05050 |
| idMR:
|
MR2137145 |
| . |
| Date available:
|
2009-09-24T11:23:45Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127985 |
| . |
| Reference:
|
[1] Chen Xue-gang, Sun Liung and Ma De-xiang: On total restrained domination in graphs.Czechoslovak Math. J. 55(130) (2005), 165–173. MR 2121664, 10.1007/s10587-005-0012-2 |
| Reference:
|
[2] E. J. Cockayne and S. T. Hedetniemi: Towards a theory of domination in graphs.Networks 7 (1977), 247–261. MR 0483788, 10.1002/net.3230070305 |
| Reference:
|
[3] E. V. Cockxne, R. M. Dawes and S. T. Hedetniemi: Total domination in graphs.Networks 10 (1980), 211–219. MR 0584887, 10.1002/net.3230100304 |
| Reference:
|
[4] G. S. Domke, J. H. Hattingh et al.: Restrained domination in graphs.Discrete Math. 203 (1999), 61–69. MR 1696234, 10.1016/S0012-365X(99)00016-3 |
| Reference:
|
[5] T. W. Haynes, S. T. Hedetniemi and P. J. Slater: Fundamentals of Domination in Graphs.Marcel Dekker Inc., New York-Basel-Hong Kong, 1998. MR 1605684 |
| Reference:
|
[6] M. A. Henning: Graphs with large restrained domination number.Discrete Math. 197/198 (1999), 415–429. Zbl 0932.05070, MR 1674878 |
| . |
