Question

Solve.

Determine how many Hamilton circuits a complete graph with 23 vertices has.
Options:

22!

23!

23

232

Answer 1

22!

Explanation:

A complete graph with N vertices has (N-1)! Hamilton circuits. Half of the circuits are mirror images of the other half, so if you're looking for unique circuits, there are actually only half this many.

N = 23

Number of Hamilton circuits = (N-1)! = (23-1)! = 22!