Question

Labelled and Unlabelled trees.

(a) How many labelled trees of order 5 are there?

(b) Draw all unlabeled tree of order 5 (under isomorphism). Hint: make cases on the diameter size.

Answer 1

a)

The number of labeled trees on n vertices is 

$T_n=n^{n-2}$

then, number of labelled trees of order 5:

$T_5=5^3=125$

b)