# Are almost all rooted trees asymmetric?

It's well known that almost all graphs are asymmetric (have trivial automorphism group) and that almost all free trees are symmetric.

By which argument do I see whether almost all rooted trees are asymmetric or symmetric?

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Did you try adapting the argument for unrooted trees, e.g. as given in en.wikipedia.org/wiki/Asymmetric_graph#Trees? –  Pete L. Clark Apr 8 '11 at 14:26