1. The problem statement, all variables and given/known data 1. up to isomorphism, there is only one 2-regular graph on 5 vertices. 2. Relevant equations 3. The attempt at a solution I am still working on the problem, but I don't understand what up to isomorphism means. Does it mean without considering isomorphism?. I just need help with that. Considering isomorphism, the first thing that comes to mind is a pentagon. The complement of this graph would also be a 2-regular on 5 vertices. Therefore, the original statement would be false.