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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.2, Problem 22ES

Textbook Problem

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Travel Use the edge-picking algorithm to design a route for the tourist in Exercise 20.

To determine

To design a route for the tourist using the edge-picking algorithm.

**Given information:**

Given, a tourist is staying in Toronto, Canada, and would like to visit four other Canadian cities by train.

The visitor wants to go from one city to the next and return to Toronto while minimizing the total travel distance.

The distances between cities, in kilometers, are given in the following table:

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And the graph is given by:

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**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 142

Hence, the edge between vertices representing Toronto and Niagara Falls having the weight 142 is marked first.

The next least weight in the graph is 174

Hence, the edge between vertices representing Kingston and Ottawa having the weight 174 is marked.

The next least weight in the graph is 259

Hence, the edge between vertices representing Toronto and Kingston having the weight 259 is marked...

Mathematical Excursions (MindTap Course List)

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