Connected Total Dominating Sets and Connected Total Domination Polynomials of Square of Paths International Journal of Mathematical Trends and Technology (IJMTT) © 2014 by IJMTT Journal Volume-11 Number-1 Year of Publication : 2014 Authors : A. Vijayan , T. Anitha Baby 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 Mathematical Trends and Technology (IJMTT). V11:56-63 July 2014. ISSN:2231-5373. www.ijmttjournal.org. Published by Seventh Sense Research Group.

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