How can I find the number of Hamiltonian cycles in a complete undirected graph?

Question

Can someone explain how to find the number of Hamiltonian cycles in a complete undirected graph?

Wikipedia says that the formula is (n-1)!/2, but when I cal

Answer 1

I think when we have a Hamiltonian cycle since each vertex lies in the Hamiltonian cycle if we consider one vertex as starting and ending cycle . we should use 2 edges of this vertex.So we have (n-1)(n-2)/2 Hamiltonian cycle because we should select 2 edges of n-1 edges which linked to this vertex.