  Let G be a simple graph of order n. The domination polynomial of G is the
polynomial D(G,x)=\sum_{i=\gamma(G)}^{n} d(G,i) x^{i}, where d(G,i) is the
number of dominating sets of G of size i, and \gamma(G) is the domination
number of G. In this paper we study the domination polynomials of cubic graphs
of order 10. As a consequence, we show that the Petersen graph is determined
uniquely by its domination polynomial.
