a21, b=6, c=10, d=25, e=27, f=9.
6. Use the numbers a, b, c, d, e, and f from your Banner number 001abcdef
to define the weights on the edges CF, AD, AC, BD, EG, and CE in the weighted
graph below, with the exception that if any of your digits are 0, you use 10 for the
weight of that edge instead.
Consider the following graph:
2
4
b
4
B
G
5
F
6
f
E
d
8
6
D
C
4
(a) Is the graph Eulerian or semi-Eulerian? Fully justify your answer.
(5 marks)
(b) If the graph is Eulerian, use Fleury's algorithm to find an Eulerian trail.
If the graph is semi-Eulerian, use a version of the algorithm to find a trail
which starts and ends at appropriate vertices and includes every edge of the
graph exactly once.
You must explain how your choices at each step are constrained by the
algorithm.
(10 marks)
(c) Find a closed walk in the graph of least weight that uses every edge at least
once; that is, solve the Chinese Postman Problem.
For full marks, that you must provide complete information showing how you
carry out each step of the algorithm, showing what choices you are making
and why you are making these choices.
(10 marks)