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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References

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