A Study on Total Rebellion Number in Graphs

Authors

  • V. Mohanaselvi Department of Mathematics, Nehru Memorial College (Autonomous), Trichy
  • P. Shyamala Anto Mary Department of Mathematics, Jayaram College of Engineering and Technology, Thuraiyur
  • A. Monisha Department of Mathematics, Nehru Memorial College (Autonomous), Trichy

DOI:

https://doi.org/10.26713/jims.v9i3.938

Keywords:

Rebellion number and Total rebellion number

Abstract

A set $R\subseteq V$ of a graph \(G = (V,E)\) is said to be a `rebellion set' (\(rb\)-set) of \(G\), if \(\arrowvert N_R(v) \arrowvert \leq \arrowvert N_{V/R}(v) \arrowvert\), for all \(v\in R\), \(\arrowvert R\arrowvert \geq \arrowvert V/R \arrowvert\) and \(\la R\ra\) has no isolated vertices. The total rebellion number \(\mathit{trb}(G)\) is the minimum cardinality of any total rebellion set in \(G\). A total rebellion set with cardinality \(\mathit{trb}(G)\) is denoted by \(\mathit{trb}(G)\)-set. In this paper, we defined the total rebellion number for simple graphs. Also, we determined its tight bounds for some standard graph and characterize this parameters.

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References

F. Harary, Graph Theory, Addison Wesley, Reading (1969).

P. Kristiansen, S.K. Hedetniemi and S.T. Hedetniemi, Alliances in graphs, J. Cobin. Ath. Cobin. Copute. 48 (2004), 157 – 177.

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V. Mohana Selvi and P. Shyamala Anto Mary, The rebellion number in graphs, International Journal of Scientific & Engineering Research 7(5) (May 2016), 56 – 62 (ISSN 2229-5518).

V. Mohana Selvi and P. Shyamala Anto Mary, National conference on bridging innovative trends in pure and applied mathematics, in: Independent Rebellion Number in Graphs, Bannari Amman Institute of Technology, Sathyamangalam (2016).

R. Kulli and B. Janakiram, The total domination number of a graph, Indian J. Pure Appl. Math. 27(6) (June 1996), 537 – 542.

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Published

2017-10-30
CITATION

How to Cite

Mohanaselvi, V., Mary, P. S. A., & Monisha, A. (2017). A Study on Total Rebellion Number in Graphs. Journal of Informatics and Mathematical Sciences, 9(3), 765–773. https://doi.org/10.26713/jims.v9i3.938

Issue

Vol. 9 No. 3 (2017)

Section

Research Articles

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