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I have n tree (acyclic graphs). If I join these n tree what will be total count of the tree? What I tried? I think if tree have ni vertex. Total tree will be:

$n_1^{(n_1-2)}*n_2^{(n_2-2)}\cdots$

But answer is wrong. What am I doing wrong?

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1 Answer 1

If you want the number of labeled trees (that is given by $n^{n-2}$ for $n$ vertices), after combining and relabeling you'd have any labelled $n_1 + n_2$ vertex tree, so $(n_1 + n_2)^{n_1 + n_2 - 2}$ in all. Or am I completely off-track here?

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