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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.

**Given information:**

The graph of Hamiltonian circuit is

**Calculation:**

- Using Greedy algorithm, the Hamiltonian circuit starting at vertices A is:
- The Hamiltonian circuit starting at vertices B is:
- The Hamiltonian circuit starting at vertices C is:
- The Hamiltonian circuit starting at vertices D is:
- The Hamiltonian circuit starting at vertices E is:

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

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

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

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

The circuit starting at E: E − D − B − C − F − A − E...

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