How can you prove that the number of spanning trees can we make from a complete graph is n^(n-2)?

Question

how we can find out that a complete graph with n nodes have n^(n-2) spanning trees?

Answer 1

This is Cayley's formula - a particular case of Kirchhoff's Theorem. Since the proof itself requires far too many symbols to be easily entered via the keyboard, I will just direct you to its Wikipedia entry:

http://en.wikipedia.org/wiki/Cayley%27s_formula

Answer 2

Use induction method.