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Remarks on restrained domination and total restrained domination in graphs

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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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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).

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