# Counting non-isomorphic graph.

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

Hint: How many non-isomorphic $2$-regular graphs are there?
• @MarkoRiedel The question asks for the number of nonisomorphic $4$-regular graphs on $7$ vertices. In that special case, the $4$-regular graphs are the complements of the $2$-regular graphs . . . oh, see dtldarek's answer! – bof Nov 29 '14 at 23:37
• (+1) $4+2 = 6 = 7-1$ I cannot believe I missed this. – Marko Riedel Nov 29 '14 at 23:59
I hope this helps $\ddot\smile$