Abstract
The restrained domination number γr(G) and the total restrained domination number γ r t (G) of a graph G were introduced recently by various authors as certain variants of the domination number γ(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 γ(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.
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Chen Xue-gang, Sun Liung and Ma De-xiang: On total restrained domination in graphs. Czechoslovak Math. J. 55(130) (2005), 165–173.
E. J. Cockayne and S. T. Hedetniemi: Towards a theory of domination in graphs. Networks 7 (1977), 247–261.
E. V. Cockxne, R. M. Dawes and S. T. Hedetniemi: Total domination in graphs. Networks 10 (1980), 211–219.
G. S. Domke, J. H. Hattingh et al.: Restrained domination in graphs. Discrete Math. 203 (1999), 61–69.
T. W. Haynes, S. T. Hedetniemi and P. J. Slater: Fundamentals of Domination in Graphs. Marcel Dekker Inc., New York-Basel-Hong Kong, 1998.
M. A. Henning: Graphs with large restrained domination number. Discrete Math. 197/198 (1999), 415–429.
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This research was supported by Grant MSM 245100303 of the Ministry of Education, Youth and Sports of the Czech Republic.
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Zelinka, B. Remarks on restrained domination and total restrained domination in graphs. Czech Math J 55, 393–396 (2005). https://doi.org/10.1007/s10587-005-0029-6
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DOI: https://doi.org/10.1007/s10587-005-0029-6