Hamilton Cycles · Example 3

Use the figure and the given Hamilton cycles to answer the following questions.
V → L → E → B → V
V → L → B → E → V
V → E → L → B → V
V → B → E → L → V

(a) Which of the Hamilton cycles (directed cycles) lie on the same cycle (undirected cycle) in the graph?
(b) Find the total weight of each cycle.
(c) Of the four, which of the Hamilton cycles describes the shortest trip for the officer? Describe the route.

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Contemporary Mathematics · §12.7 Hamilton Cycles · Example 3