Counting the number of asymmetric graphs on n nodes? Asymmetric graph is a graph that has only trivial automorphism. Asymptotically, almost all finite graphs are asymmetric. I'm looking for upper bounds and lower bounds on the growth rate of the number of asymmetric graphs on n nodes. Also, I'm looking for a function $f(n)$ that exactly counts the number of asymmetric graph on n nodes? Is this function efficiently computable?

You might look at the references in A003400 for possibly disconnected graphs and A124059 for connected ones. Neither gives a formula, even asymptotic.