Counting non-isomorphic graph.

Question

How many exists non-isomorphic 4-regular graphs $G = (V,E)$ where $|V|=7$ vertices?

I'm asking for hint to solve it with group theory( if it is possible) and without them

Answer 1

Hint: How many non-isomorphic $2$-regular graphs are there?

Answer 2

Hint:

• How does a complement of such a graph looks like?
• How many such non-isomorphic complements exist?

I hope this helps $\ddot\smile$