  Let G=(V,E) be a simple graph. A set S\subset V is a dominating set of G, if
every vertex in V\S is adjacent to at least one vertex in S. Let {\mathcal
C}_n^i be the family of dominating sets of a cycle C_n with cardinality i, and
let d(C_n,i) = |{\mathcal C}_n^i. In this paper, we construct {\mathcal C}_n^i,
and obtain a recursive formula for d(C_n, i). Using this recursive formula, we
consider the polynomial D(C_n, x) = \sum_{i=1}^n d(C_n, i)x^i, which we call
domination polynomial of cycles and obtain some properties of this polynomial.
