33 Cayley’s formula for the number of trees

Theorem 33.1 First proof (bijection)

There are \(n^{n - 2}\) different labeled trees on \(n\) nodes.

Proof ▶

TODO

Theorem 33.2 Second proof (Linear Algebra)

There are \(n^{n - 2}\) different labeled trees on \(n\) nodes.

Proof ▶

TODO

Theorem 33.3 Second proof (Recursion)

There are \(n^{n - 2}\) different labeled trees on \(n\) nodes.

Proof ▶

TODO

Theorem 33.4 Second proof (Double Counting)

There are \(n^{n - 2}\) different labeled trees on \(n\) nodes.

Proof ▶

TODO