Interestingly (and perhaps obviously?), For n > 2, a(n) = A124059(n-1).
Table of n, a(n) for n=1..11.
Eric Weisstein's World of Mathematics, Graph Automorphism
Eric Weisstein's World of Mathematics, Identity Graph
a(n) = A003400(n) - A124059(n).
For n > 2, a(n) = A124059(n-1) (conjectured; perhaps provable/obvious?).
Cf. A003400 (not-necessarily connected simple asymmetric graphs).
Cf. A124059 (connected simple asymmetric graphs).
Sequence in context: A061899 A134492 A067421 * A124059 A052764 A024284
Adjacent sequences: A275864 A275865 A275866 * A275868 A275869 A275870
Eric W. Weisstein, May 19 2017