On isolate domination in hypergraphs

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DOI:

https://doi.org/10.26637/mjm1001/005

Abstract

In this paper we introduced the notion of an isolate domination in hypergraphs. A set DV is called a dominating set of H if for every vVD there exists uD such that u and v are adjacent. A dominating set I of a hypergraph H is called an isolate dominating set of H if it contains at least one vertex vI such that v is not adjacent to any vertex of I. The minimum cardinality of an isolate dominating set of H is called the isolate domination number γ0 of  H. We determine the isolate domination number for some hypergraphs while the study on this parameter has been initiated. Furthermore, the effects of the removal of a vertex or an edge from the hypergraph upon the isolate domination number are examined.

Keywords:

Hypergraphs, domination number, isolate domination

Mathematics Subject Classification:

05C65
  • Kishor Pawar Kavayitri Bahinabai Chaudhari North Maharashtra University: Jalgaon, Maharashtra, India.
  • Megha M. Jadhav Kavayitri Bahinabai Chaudhari North Maharashtra University, Jalgaon, India.
  • Pages: 55-62
  • Date Published: 01-01-2022
  • Vol. 10 No. 01 (2022): Malaya Journal of Matematik (MJM)

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Published

01-01-2022

How to Cite

Kishor Pawar, and M. M. Jadhav. “On Isolate Domination in Hypergraphs”. Malaya Journal of Matematik, vol. 10, no. 01, Jan. 2022, pp. 55-62, doi:10.26637/mjm1001/005.