   # Use the edge-picking algorithm to find a Hamiltonian circuit in the graph in Exercise 2. How does the weight of this circuit compare with the weights of the circuits found in Exercise 2? ### 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 3EE
Textbook Problem
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## Use the edge-picking algorithm to find a Hamiltonian circuit in the graph in Exercise 2. How does the weight of this circuit compare with the weights of the circuits found in Exercise 2?

To determine

The Hamiltonian circuits using greedy algorithm starting at each vertex and the Hamiltonian circuits using edge-picking algorithm and compare with the two weights of the circuits.

### 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.

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

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

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