Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
domination number; domatic number; total domination number; total domatic number; restrained domination number; restrained domatic number; total restrained domination number; total restrained domatic number
domination number; domatic number; total domination number; total domatic number; restrained domination number; restrained domatic number; total restrained domination number; total restrained domatic number
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.
References:
[1] Chen Xue-gang, Sun Liung and Ma De-xiang: On total restrained domination in graphs. Czechoslovak Math. J. 55(130) (2005), 165–173. DOI 10.1007/s10587-005-0012-2 | MR 2121664
[2] E. J. Cockayne and S. T. Hedetniemi: Towards a theory of domination in graphs. Networks 7 (1977), 247–261. DOI 10.1002/net.3230070305 | MR 0483788
[3] E. V. Cockxne, R. M. Dawes and S. T. Hedetniemi: Total domination in graphs. Networks 10 (1980), 211–219. DOI 10.1002/net.3230100304 | MR 0584887
[4] G. S. Domke, J. H. Hattingh et al.: Restrained domination in graphs. Discrete Math. 203 (1999), 61–69. DOI 10.1016/S0012-365X(99)00016-3 | MR 1696234
[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
[6] M. A. Henning: Graphs with large restrained domination number. Discrete Math. 197/198 (1999), 415–429. MR 1674878 | Zbl 0932.05070
Search
Partner of
