# Lower bound on number of $r$-regular graphs witn $n$ vertices

Consider the set of $r$-regular labeled graphs with $n$ vertices. There are results on its asymptotic size (see for instance this question on MO).

Is there a known, explicit lower bound on that size, valid for any $r$ and $n$?

• It is easy to see that once you have your $N(r, n_0)=a>1,$ then $N(r, k n_0) \geq a^k.$ – Igor Rivin Mar 20 '17 at 16:37