Finding the number of unlabeled graphs with $n$ vertices such that each vertex has degree 2 I'm trying to find the number of unlabeled graphs with $n$ vertices such that each vertex has degree 2. I know that the edge set for such a graph will have cardinality $n$ and that the maximum number of possible edges for any graph with n vertices is  ${n}\choose{2}$ but I'm not exactly sure how to proceed from here. 

Hint: A graph on $n$ vertices with each vertex having degree $2$ is simply a graph consisting of disjoint cycles. If the vertices are unlabeled, all you care about are the lengths of each cycle. 
