Trees

Question

Number of rooted labeled trees(i.e. each node can be the root) with  6 vertices is:

Comments

Usintg cayley theorem = n^n-2 = 6⁴

since any of 6 can be root ,So total = 6⁴ $\times$​ 6​​​​​​ 

Number of rooted labeled trees 132 $\times$ 6!

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https://gatecse.in/number-of-binary-trees-possible-with-n-nodes/

Answer 1

Number of labeled trees of n nodes is $n^{n-2}$

Now when each node can be root so for root we have n choices

Thus $n^{n-2}$*n=$n^{n-1}$

For n=6 7776 tree are possible

Comments

yes, i also think so..

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yes, thankyou Shivam!

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@joshi_nitish and @Tesla! Thanks to both of you. Many questions about trees are cleared by this discussion.