Independent partial domination

  • L. Philo Nithya Department of Mathematics, Christ University, Bengaluru, Karnataka, India.
  • Joseph Varghese Kureethara Department of Mathematics, Christ University, Bengaluru, Karnataka, India.
Keywords: Domination chain, independent partial dominating set, partial independent set

Abstract

For \(p\in(0,1]\), a set \(S\subseteq V\) is said to \(p\)-dominate or partially dominate a graph \(G = (V, E)\) if \(\frac{|N[S]|}{|V|}\geq p\). The minimum cardinality among all \(p\)-dominating sets is called the \(p\)-domination number and it is denoted by \(\gamma_{p}(G)\). Analogously, the independent partial domination (\(i_p(G)\)) is introduced and studied here independently and in relation with the classical domination. Further, the partial independent set and the partial independence number \(\beta_p(G)\) are defined and some of their properties are presented. Finally, the partial domination chain is established as \(\gamma_p(G)\leq i_p(G)\leq \beta_p(G) \leq \Gamma_p(G)\).

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Published
2021-12-01
How to Cite
[1]
L. Philo Nithya and J. V. Kureethara, “Independent partial domination”, CUBO, vol. 23, no. 3, pp. 411–421, Dec. 2021.
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Articles