Trees

Question

There are n^n-2 labeled trees with n vertices(n>2)

Can anyone explain it with complete proof?

Answer 1

There are n^n-2 labeled tree with n vertices

In a tree with 3 nodes we can have 3 labeled tree

suppose there a three nodes 1,2,3

1-2-3  ,  1-3-2 and 2-1-3

if n=3 we have 3^3-2=3 labeled trees

In a tree with 4 nodes we can have 16 labeled tree

In a tree with 5 nodes we can have 125 labeled tree