A 12 4 6 2 C TO D a) How many distinct Hamilton circuits are associated with this graph? b) Use the Brute-force Method to cost out the Hamilton circuits and identify the optimal Hamilton circuit. Show all your work. c) Rewrite the optimal Hamilton circuit found in part b starting from vertex B. d) Use the Nearest-Neighbor Method, starting from vertex A, to create a Hamilton Circuit. e) What is the weight of the circuit? f) Is this the optimal Hamilton Circuit? g) In your opinion, which method, Brute-Force or Nearest-Neighbor, is the best method for finding a Hamilton circuit for this graph? Explain your