Article Published In Vol.4 (May-June-2016)

Connected Total Dominating Sets and Connected Total Domination Polynomials of Triangular Ladders

Author : A. Vijayan and T. Anitha Baby

Let G be a simple connected graph of order n. Let D_ct(G, i) be the family of connected total dominating sets of G with cardinality i. The polynomial D_ct (G, x) = d_ct (G, i) xⁱ is called the connected total domination polynomial of G. In this paper, we study some properties of connected total domination polynomials of the Triangular Ladder TL_n. We obtain a recursive formula for d_ct (TL_n, i). Using this recursive formula, we construct the connected total domination polynomial    D_ct (TL_n, x) = d_ct(TL_n, i) xⁱ , of TL_n, where d_ct(TL_n, i) is the number of connected  total dominating sets of TL_n with cardinality i and some properties of this polynomial have been studied.

Keywords: Triangular Ladder, connected total dominating set, connected total domination number, connected total domination polynomial.