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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 11 | Number 1 | Year 2014 | Article Id. IJMTT-V11P507 | DOI : https://doi.org/10.14445/22315373/IJMTT-V11P507

Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths


A. Vijayan, T. Anitha Baby
Abstract

Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets in G with cardinality i. The polynomial Dct (G, x) = nΣdcti=γct(G) (G, i) xi is called the connected total domination polynomial of G. In this paper, we obtain a recursive formula for dct (Pn2 , i). Using this recursive formula, we construct the connected total domination polynomial Dct (Pn2 , x) =nΣi=[n-3/2] dct( Pn2, i) xi , where dct (Pn2 , i) is the number of connected total dominating sets of of cardinality i and some properties of this polynomial have been studied.

Keywords
Square of Path, connected total dominating set, connected total domination number, connected total domination polynomial.
References

[1] S. Alikhani and Y.H. Peng, Domination sets and Domination polynomials of cycles, Global Journal of pure and Applied Mathematics vol.4 no.2, 2008.
[2] S. Alikhani and Y.H. Peng, Dominating sets and Domination polynomials of paths, International journal of Mathematics and mathematical sciences, 2009.
[3] S. Alikhani and Y.H. Peng, Introduction to Domination polynomial of a graph, arXiv : 0905.225 [v] [math.co] 14 may, 2009.
[4] G. Chartrand and P. Zhang, Introduction to Graph theory, McGraw-Hill, Boston, Mass, USA, 2005.
[5] Maryam Atapour and Nasrin Soltankhah, On Total Domination sets in Graphs, Int. J. Contemp. Math. sciences, 2009, Vol.4, no.6, 253-257.
[6] A. Vijayan and S. Sanal Kumar, On Total Domination Sets and Polynomials of Paths, International Journal of Mathematics Research, Vol.4, no.4 (2012), pp. 339-348.
[7] A. Vijayan, K.Lal Gipson, Dominating sets and Domination Polynomials of square of paths, open Journal of Discrete Mathematics, 2013, 3, 60-69.

Citation :

A. Vijayan, T. Anitha Baby, "Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths," International Journal of Mathematics Trends and Technology (IJMTT), vol. 11, no. 1, pp. 56-63, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V11P507

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