This article extends the notion of restrained domination from graphs to hypergraphs, establishing bounds for the restrained domination number in hypergraphs. The study investigates the connection between the restrained domination number and the domination number, particularly aiming to pinpoint hypergraph classes where these two parameters are identical. We give precise values for the restrained domination number for various hypergraph classes and introduce a family \(\mathcal {F}\) of hypergraphs where the restrained domination number and the domination number are distinct. Additionally, we investigate the relationship between the domination number of a hypergraph \(\mathcal {H}\) and its complement \(\overline{\mathcal {H}}\) , showing that for r-uniform hypergraphs with \(\gamma (\overline{\mathcal {H}})\ge 3\) , the restrained domination number and domination number are equal. Our work generalizes several results from graph theory to hypergraph theory, contributing to a deeper understanding of hypergraph properties.

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On Restrained Domination in Hypergraphs

  • Puran Dangal,
  • Biswajit Deb,
  • Kaushol Pradhan

摘要

This article extends the notion of restrained domination from graphs to hypergraphs, establishing bounds for the restrained domination number in hypergraphs. The study investigates the connection between the restrained domination number and the domination number, particularly aiming to pinpoint hypergraph classes where these two parameters are identical. We give precise values for the restrained domination number for various hypergraph classes and introduce a family \(\mathcal {F}\) of hypergraphs where the restrained domination number and the domination number are distinct. Additionally, we investigate the relationship between the domination number of a hypergraph \(\mathcal {H}\) and its complement \(\overline{\mathcal {H}}\) , showing that for r-uniform hypergraphs with \(\gamma (\overline{\mathcal {H}})\ge 3\) , the restrained domination number and domination number are equal. Our work generalizes several results from graph theory to hypergraph theory, contributing to a deeper understanding of hypergraph properties.