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Let G be a simple connected graph of order m. Let D2(G, i)
be the family of 2-dominating sets in G with cardinality i. The polynomial
D2(G, ) = is called the 2-domination polynomial of G. In this paper we obtain a recursive formula for d2(Cm, i). Using this
recursive formula we construct the 2-domination polynomial,
D2(Cm,) = , where d2(Cm, i) is the number of 2-dominating sets of Cm of cardinality i and some properties of this polynomial have been studied.
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