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

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) = ^{n}Σdct_{i=γct(G)} (G, i) x^{i} is called the connected total domination polynomial of G. In this paper, we obtain a recursive formula for d_{ct} (P_{n}^{2} , i). Using this recursive formula, we construct the connected total domination polynomial Dct (P_{n}^{2} , x) =^{n}Σ_{i=[n-3/2]} dct( P_{n}^{2}, i) xi , where dct (P_{n}^{2} , i) is the number of connected total dominating sets of of cardinality i and some properties of this polynomial have been studied.**References**

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**Keywords**

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