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