A Review on Relation between Dominating and
Total Dominating Color Transversal Number of
Graph and Monotonicity

J.Sangeetha; R.Jeyamani

doi:https://doi.org/10.14445/22315373/IJMTT-V44P503

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 44 | Number 1 | Year 2017 | Article Id. IJMTT-V44P503 | DOI : https://doi.org/10.14445/22315373/IJMTT-V44P503

A Review on Relation between Dominating and Total Dominating Color Transversal Number of Graph and Monotonicity

J.Sangeetha, R.Jeyamani

Citation :

J.Sangeetha, R.Jeyamani, "A Review on Relation between Dominating and Total Dominating Color Transversal Number of Graph and Monotonicity," International Journal of Mathematics Trends and Technology (IJMTT), vol. 44, no. 1, pp. 23-27, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V44P503

Abstract

Domination is a very fast developing area in Graph Theory. This paper deals with combination of domination, total domination, proper colouring and transversal sets. Also demonstrate the domination transversal number for different types of graphs. We also extend some relation between domination and total domination colour transversal number of graphs. We also provide some examples to justify our results. We also obtain an upper bound of this number which increases monotonically.

Keywords

Domination, Total domination, Transversal sets, Proper colouring.

References

[1]. T. W. Haynes, S. T. Hedetniemi, and P. J. Slater, Domination in graphs: Advanced topics, Mercel Dekker, New York, 1998.
[2]. S. Thomasse and A. Yeo, Total domination of graphs and small transversals of hyper graphs, Combinatorica 27 (2007), 473-487.
[3]. M. Chellali and T. W. Haynes, A note oSSSSn the total domination number of a tree, J. Combin. Math. Combin. Computer 58 (2006), 189-193.
[4] D. B. West. Introduction to Graph Theory. Prentice Hall,1996.
[5] D. K. Thakkar and A. B. Kothiya, Total Dominating Color Transversal number of Graphs, Annals of Pure and Applied Mathematics, Vol. 11(2), 2016, 39 – 44.
[6] R. L. J. Manoharan, Dominating colour transversals in graphs, Bharathidasan University, September, 2009.
[7] D.K.Thakkar and A.B.Kothiya, Relation between Total Dominating Color Transversal number and Chromatic number of a Graph, Communicated for publication in AKCE International Journal of Graphs and Combinatorics.
[8] Michael A. Henning and Andres Yeo, Total Domination in Graphs, Springer, 2013.
[9] D.K.Thakkar and K.N.Kalariya, Strong vertex covering in hypergraph, Annals of Pure and Applied Mathematics, 11(1) (2016) 123- 131.
[10] V.R.Kulli and B.Janakiram, Total global domination number of a graph, Indian Journal of Pure and Applied Math., 27(6) (1996) 537-542.
[11] Sandi Klavzar, Coloring Graph Products-A survey, Elsevier Discrete Mathematics, 155(1996), 135-145.
[12] David Amos, On total domination in graphs, University of Houston Downton, December 2012.
[13] Goksen BACAK, “Vertex Color of a Graph”, Master of Science Thesis, ˙IZM˙IR, December, 2004.
[14] Dr. S. Sudha and R. Alphonse Santhanam, “Total Domination on Generalised Petersen Graphs”, International Journal of Scientific and Innovative Mathematical Research (IJSIMR) Volume 2, Issue 2, February 2014, PP 149-155.