About Isolate Inclusive Sets in Graphs


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Authors

  • D. K. Thakkar Department of Mathematics, Saurashtra University Campus, University Road, Rajkot, Gujarat, India
  • N. J. Savaliya Department of Mathematics, Saurashtra University Campus, University Road, Rajkot, Gujarat, India

Keywords:

Isolate dominating set, minimal isolate dominating set, minimum isolate dominating set, isolate domination number, isolate inclusive set, private neighbourhood

Abstract

In this paper we further study isolate domination in graphs. In particular we study the effect of removing an edge from the graph on the isolate domination number of the graph. We prove a necessary and sufficient condition under which the isolate domination number increases when an edge is removed from the graph. Further we also prove a necessary and sufficient condition under which the isoinc number increases when an edge is removed from the graph. We also consider the graphs for which isolate dominating number is equal to 1 or 2.

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Published

15-06-2018

How to Cite

D. K. Thakkar, & N. J. Savaliya. (2018). About Isolate Inclusive Sets in Graphs. International Journal of Mathematics And Its Applications, 6(2 - B), 361–367. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/734

Issue

Vol. 6 No. 2 - B (2018)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.