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

  1. P. David, summer and pattie blitch ,Domination critical graph, Journal of combinatorial theory series B, 34, (1983).
  2. F. Harary, Graph Theory, Addison-Wesley, reading Mass, (1969).
  3. V. R. Kulli, B. Janikiram, The nonsplit domination number of a graph, Indian J. Pure Appl. Math., 31, 545–550 (2000).
  4. M. Lemanska, A. Patyk, Weakly Connected Domination Critical graphs, Opuscula Mathematica, 28, 325–330 (2008).
  5. R. C. Brigham, P. Z. Chinn, R. D. Dutton, Vertex domination critical graphs, networks, 18, 173–179 (1988).
  6. D. P. Sumner, Critical concepts in domination, Discrete Math., 86, 33-46 (1990).
  7. X. Gang, L. Sun, D. Xiang, Connected Domination Critical graphs, Applied Mathematics, 17, 503–507 (2004).
Global Analysis and Discrete Mathematics
Volume 7, Issue 1
November 2022
Pages 109-115

Files

History

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

Share

How to cite

Statistics