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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 53 | Number 6 | Year 2018 | Article Id. IJMTT-V53P557 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P557

A Note on Chromatic Weak Dominating Sets in Graphs


P. Selvalakshmi, S. Balamurugan
Abstract

In this paper chromatic weak dominating sets and chromatic weak domination number are de ned. Chromatic weak domination number for standard graphs are found, bounds for chromatic weak domination number are obtained.

Keywords
Domination, Weak domination, Chromatic weak domination, Chromatic number.
References

[1] S. Balamurugan, P. Aristotle and V. Swaminathan, Chromatic Strong dominating sets in Bipartite graphs, AKCE International Journal of Graphs and Combinatorics, Submitted.
[2] S. Balamurugan, G. Prabakaran and V. Swaminathan, On Chromatic Strong Dominating Sets in Graphs, International Journal of Engineer- ing Science, Advanced Computing and Bio - Technology, Vol 3. Issue 3(2011), 139 - 149.
[3] S. Balamurugan, A. Wilson Baskar and V. Swaminathan, Equality of strong domination and chromatic strong domination in graphs, Interna- tional Journal of Mathematics and Soft Computing, Vol. 1. No. 1(2011), 69 - 76.
[4] Dieter Gernert, Inequalities between the domination number and the chromatic number of a graph, Discrete Math . 76 (1989) 151-153.
[5] F. Harary, Graph Theory, Addison Wesley , reading Mass (1972).
[6] J. H. Hattingh and M. A. Henning, On strong domination in graphs, J. Combin.Math. Comb. Comput. 26 (1998) 73 - 82.
[7] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Decker Inc.. New york, 1998.
[8] M. Poobalaranjani, On Some Coloring and Domination Parameters in Graphs, Ph.D Thesis, Bharathidasan University, India, 2006.
[9] E. Sampathkumar, L. Pushpa Latha, Strong weak domination and dom- ination balance in a graph, Discrete Mathematics, 161 (1996), 235 - 242.
[10] P. Thangaraju, Studies in Domination in graphs and Degree sequences, Thesis, Nov., (2001).

Citation :

P. Selvalakshmi, S. Balamurugan, "A Note on Chromatic Weak Dominating Sets in Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 53, no. 6, pp. 464-475, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V53P557

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