   # Continue investigating Hamiltonian circuits in Figure 5.12 by using the greedy algorithm starting at vertices C, D, and E. Then compare the various Hamiltonian circuits to identify the one with the 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 1EE
Textbook Problem
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## Continue investigating Hamiltonian circuits in Figure 5.12 by using the greedy algorithm starting at vertices C, D, and E. Then compare the various Hamiltonian circuits to identify the one with the smallest total weight.

To determine

The Hamiltonian circuits using greedy algorithm starting at vertices C, D and E. Then compare the various Hamiltonian circuits to identify the one with the smallest total weight.

### Explanation of Solution

Calculation:

The graph of Hamiltonian circuit is

Using Greedy algorithm, the Hamiltonian algorithm starting at vertices C is:

1. Start at C, travel along the smallest weight edges, continue this until travel all vertices.
2. Therefore the Hamiltonian circuit is C − A − B − E − D − C.

Total weight of this circuit is 3 + 5 + 1 + 2 + 7 = 18

3. Start at D, travel along the smallest weight edges, continue this until travel all vertices...

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