On isolate domination in hypergraphs

Kishor Pawar; Megha M. Jadhav

doi:10.26637/mjm1001/005

Abstract

In this paper we introduced the notion of an isolate domination in hypergraphs. A set $D \subseteq V$ is called a dominating set of $\mathcal{H}$ if for every $v \in V \setminus D$ there exists $u \in D$ such that $u$ and $v$ are adjacent. A dominating set $I$ of a hypergraph $\mathcal{H}$ is called an isolate dominating set of $\mathcal{H}$ if it contains at least one vertex $v \in I$ such that $v$ is not adjacent to any vertex of $I$. The minimum cardinality of an isolate dominating set of $\mathcal{H}$ is called the isolate domination number $\gamma_{0}$ of $\mathcal{H}$. 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

Authors Imprint References Funding Related Articles Downloads

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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