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.

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The number of labeled trees on n vertices is

$T_n=n^{n-2}$

then, number of labelled trees of order 5:

$T_5=5^3=125$

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