k-Isolate Domination Number of Splitting Graph of Simple Graphs

G. Rajasekar1 and A. Jeslet Kani Bala1

1Department of Mathematics, Jawahar Science College, Neyveli, Tamilnadu, India.

Abstract: A dominating set $S$ of a graph $G$ is said to be a $k$-isolate dominating set if $\left\langle S \right\rangle$ has at least $k$-isolated vertices [4]. In this paper the $k$-isolate dominating set of splitting graph of some graphs such as path, cycle and complete graphs are found.
Keywords: Dominating set, Isolate dominating set, $k$-isolate dominating set, $k$-isolate domination number, splitting graph, path, cycle and complete graph.

Cite this article as: G.Rajasekar and A. Jeslet Kani Balak-Isolate Domination Number of Splitting Graph of Simple Graphs, Int. J. Math. And Appl., vol. 9, no. 2, 2021, pp. 13-16.

References
1. I. Sahul Hamid and S. Balamurugan, Isolate domination in graphs, Arab Journal of Mathematical Sciences, 22(2016), 232-241.
2. E. Sampathkumar and H. B. Walikar, On Splitting Graph of a Graph, J. Karnatak Univ. Sci., 25(13)(1980), 13-16.
3. H. P. Patil and S. Thangamari, Miscellaneous Properties of splitting graphs and Related concepts, in Proceedings of the National workshop on Graph Theory and its Application, Manonmaniam Sundaranar University, Tirunelveli, February 21-27, (1996), 121-128.
4. G. Rajasekar and A. Jeslet Kani Bala, $k-$Isolate Domination Number of Simple Graphs, Malaya Journal of Matematik, S(1)(2019), 113-115.
5. G. Rajasekar and A. Jeslet Kani Bala, $k-$Isolate Domination Number of Graphs inherited from Cycle Graph, The International Journal of Analytical and Experimental Modal Analysis, XI(X)(2019), 213-218.

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