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