2SSD (G). The 2-step secure dominating set of G is found for path, cycle, ladder graph, Peterson graph, wheel graph, Helm graph, closed helm graph.

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2-Step Secure Domination on Graphs

J. E. Jenolin*, S. M. Ambika**, B. Uma Devi***
*-*** Department of Mathematics, S.T. Hindu College, Nagercoil, Tamilnadu, India.
Periodicity:July - December'2021
DOI : https://doi.org/10.26634/jmat.10.2.18416

Abstract

This paper introduces a new parameter called 2-step secure domination of a graph with real world applications. Let G = (V, E) be a graph. A subset D of a vertices in a graph G is 2-step secure dominating set if every vertex v ϵ V - D, there exist one vertex uϵD such that d(u, v) = 2, and if each vertex uϵV-D is adjacent to a vertex vϵD such that (D-{v})υ{u} is a dominating set. The minimum cardinality of such a set is called the 2-step secure domination G, denoted by γ2SSD (G). The 2-step secure dominating set of G is found for path, cycle, ladder graph, Peterson graph, wheel graph, Helm graph, closed helm graph.

Keywords

Domination, 2-Step Domination, Secure Domination, 2-Step Secure Domination.

How to Cite this Article?

Jenolin, J. E., Ambika, S. M., & Devi, B. U. (2021). 2-Step Secure Domination on Graphs. i-manager's Journal on Mathematics, 10(2), 30-36. https://doi.org/10.26634/jmat.10.2.18416

References

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