A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists
of one or more (disconnected) cycles.

The numbers
of two-regular graphs on , 2, ... nodes are 0, 0, 1, 1, 1, 2, 2, 3, 4, 5, ... (OEIS
A008483), which are equivalent to the numbers
of partitions of
into parts .
The first few such graphs are illustrated above.