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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 25ES

Textbook Problem

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Travel Use the edge-picking algorithm to find a low-cost route for the traveler in Exercise 23.

To determine

To find a low-cost route for the tour using the edge-picking algorithm.

**Given information:**

Given, Nicole wants to tour Asia.

She will start and end her journey in Tokyo and visit Hong Kong, Bangkok, Seoul, and Beijing.

The airfares available to her between cities are given in the table below:

â€ƒâ€ƒ

And the graph is given by:

â€ƒâ€ƒ

**Calculation:**

A path in a Hamiltonian graph is said to be a Hamiltonian Circuit if it begins and ends at the same vertex and passes through each vertex of a graph exactly once.

The edge-picking algorithm states to mark the edge that has the smallest weight in the complete graph. Then, the edge with the next smallest weight is marked as long as it does not complete a circuit and does not add a third marked edge to a single vertex. This process continues till no longer an edge can be marked. Then the final edge completing the Hamiltonian circuit is marked.

Here, the least weight in the graph is 225

Hence, the edge between vertices representing Seoul and Beijing having the weight 225 is marked first.

The next least weight in the graph is 320

Hence, the edge between vertices representing Hong Kong and Bangkok having the weight 320 is marked...

Mathematical Excursions (MindTap Course List)

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