# Simple and 2-regular graph with exactly n vertices

How do i approach this problem:

For which natural numbers $n$ there exists a simple, 2-regular graph with exactly $n$ vertices?

-

The logic will work for every single $n$. For example, it suffices to consider: is there a 0-cylce? How about a 1-cycle? How about a 2-cycle? –  Calvin Lin Jan 31 '13 at 5:40