An asymptotic formula for the number of asymmetric graphs

A general formula giving an asymptotic expansion for the number $N(n)$ of identity graphs with $n$ vertices, as $n\to\infty$, is obtained. Two terms of this asymptotic expansion are given in an explicit form. The obtained formula estimates the rate of convergence in the Pólya effect [F. Harary and E. M. Palmer, Graphical enumeration (1973; Zbl 0266.05108)] that almost all undirected graphs have the trivial automorphism group as $n\to\infty$.