   # Use the greedy algorithm and the weighted graph below to generate a Hamiltonian circuit starting from each vertex. Then compare the different circuits to find the one of smallest total weight. ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.2, Problem 2EE
Textbook Problem
493 views

## Use the greedy algorithm and the weighted graph below to generate a Hamiltonian circuit starting from each vertex. Then compare the different circuits to find the one of smallest total weight. To determine

The Hamiltonian circuits using greedy algorithm starting at each vertex. Then compare the various Hamiltonian circuits to identify the one with the smallest total weight.

### Explanation of Solution

Given information:

The graph of Hamiltonian circuit is

Calculation:

1. Using Greedy algorithm, the Hamiltonian circuit starting at vertices A is:
2. The circuit starting at A: A − F − C − D − E − B − A.

Total weight of this circuit is 8 + 7 + 8 + 3 + 15 + 24 = 65

3. The Hamiltonian circuit starting at vertices B is:
4. The circuit starting at B: B − D − E − F − C − A − B.

Total weight of this circuit is 5 + 3 + 16 + 7 + 11 + 24 = 66

5. The Hamiltonian circuit starting at vertices C is:
6. The circuit starting at C: C − F − A − D − E − B − C.

Total weight of this circuit is 7 + 8 + 20 + 3 + 15 + 17 = 70

7. The Hamiltonian circuit starting at vertices D is:
8. The circuit starting at D: D − E − B − C − F − A − D...

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