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Remarks on restrained domination and total restrained domination in graphs

Czechoslovak Mathematical Journal volume 55, pages 393–396 (2005)Cite this article

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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Authors and Affiliations

  1. Dept. of Applied Mathematics, Technical University of Liberec, Voronezska 13, 461 17, Liberec, Czech Republic

    Bohdan Zelinka

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  1. Bohdan Zelinka
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Additional information

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

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