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

Abstract

Let G be a simple connected graph of order n. Let Dct(G, i) be the family of connected total dominating sets of G with cardinality i. The polynomial Dct (G, x) = ∑_(i = γ_ct (G))^ndct (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 TLn. We obtain a recursive formula for dct (TLn, i). Using this recursive formula, we construct the connected total domination polynomial    Dct (TLn, x) = ∑_(i =n-1)^"2n" dct(TLn, i) xi , of TLn, where dct(TLn, i) is the number of connected  total dominating sets of TLn with cardinality i and some properties of this polynomial have been studied.