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We have a complete Graph G with |V|=n . We know it has n^(n-2) possible spanning trees. How many of them could be split into two equal halves by removing a single edge?

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After some thought:

It's Choose(n n/2) * (((n/2)^(n/2 - 2))^2) * (n/2)^2

Pick the set of vertices that will remain on one side after splitting

Choose (n n/2)

How many spanning trees could exist on that group?

m = n/2, * = m^(m-2)

We have two sets :

(*)^2

Connect the two sets by two vertices each on each set:

(n/2)^2

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