Number of isomorphism classes of a tree on n vertices I'm currently trying to solve this problem:
"Show that the number of isomorphism classes of tree on n vertices is at least $\frac{n^{n-2}}{n!}$."
I'm pretty stumped to be honest.  I know of Cayley's formula; there are $n^{n-2}$ trees on n labelled vertices, so I'm guessing that this may come in handy.  
One idea I had was to find the most number of isomorphism classes.  This, I believe, should be n-2, for $n \geq 2$, and 1, for $n=0, 1$.  But then I don't particularly think this would be of any use or would lead to a very forced way to prove it.
Any hints / ideas? 
Thanks!

$n^{n-2}$ is smaller than or equal to the number of isomorphism classes times $n!$ because all trees in an isomorphism class are given by a permutation of the vertices, so your bound is a lower bound on the number of isomorphism classes.
