Inverse isolate domination number on a vertex switching of cycle related graphs

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DOI:

https://doi.org/10.26637/MJM0804/0172

Abstract

Let \(G\) be non-trivial graph. A subset \(S \subset V(G)\) is called a isolate dominating set of \(G\) if is a dominating set and \(\delta(<S>)=0\). The set \(S^{\prime} \subset V(G)-S\) such that \(S^{\prime}\) is a dominating set of \(G\) and \(\delta\left(<S^{\prime}>\right)=0\), then \(S^{\prime}\) is called an inverse isolate dominating set with respect to \(S\). The minimum cardinality of an inverse isolate dominating set is called an inverse isolate dominating number and is denoted by \(\gamma_0^{-1}(G)\). In this paper we find inverse isolate dominating number on vertex switching of some cycle related graphs.

Keywords:

Domination, Isolate domination, Inverse domination, Switching

Mathematics Subject Classification:

Mathematics
  • C. Jayasekaran Department of Mathematics, Pioneer Kumaraswamy College, Nagercoil-629003, Kanyakumari District, Tamil Nadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012.
  • A. Vijila Rani Department of Mathematics, Pioneer Kumaraswamy College, Nagercoil-629003, Kanyakumari District, Tamil Nadu, India. Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli-627012.
  • Pages: 2309-2314
  • Date Published: 01-10-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

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Published

01-10-2020

How to Cite

C. Jayasekaran, and A. Vijila Rani. “Inverse Isolate Domination Number on a Vertex Switching of Cycle Related Graphs”. Malaya Journal of Matematik, vol. 8, no. 04, Oct. 2020, pp. 2309-14, doi:10.26637/MJM0804/0172.