Nonsplit Domination Vertex Critical Graph

Document Type : Research Paper

Authors

1 PES University

2 Siddaganga Institute of technology

Abstract

A dominating set D of a graph G = (V, E) is a nonsplit dominating set if the induced graph ⟨V − D⟩ is connected. The nonsplit domination number γns(G) is the minimum cardinality of a nonsplit domination set. The purpose of this paper is to initiate the investigation of those graphs which are critical in the following sense: A graph G is called vertex domination critical if γ(G − v) < γ(G) for every vertex v in G. A graph G is called vertex nonsplit critical if γns(G −v) < γns(G) for every vertex v in G. Initially we test whether some particular classes of graph are γns-critical or not and then we have shown that there is no existence of 2-γns-critical graph. Then 3-γns-critical graphs are characterized.

Keywords

References

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Analytical and Numerical Solutions for Nonlinear Equations
Volume 7, Issue 1
November 2022
Pages 109-115

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History

  • Receive Date: 16 March 2022
  • Revise Date: 19 November 2022
  • Accept Date: 22 May 2022

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