   # Travel Use the edge-picking algorithm to find a low-cost bus route in Exercise 24. ### 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 26ES
Textbook Problem
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## Travel Use the edge-picking algorithm to find a low-cost bus route in Exercise 24.

To determine

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

### Explanation of Solution

Given information:

Given, the prices for travelling between five cities in Colorado by bus are given in the table below:

The travel starts and ends in Boulder and visits each city.

And the graph is given by:

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 16

Hence, the edge between vertices representing Boulder and Denver having the weight 16 is marked first.

The next least weight in the graph is 22

Hence, the edge between vertices representing Denver and Colorado Springs having the weight 22 is marked.

The next least weight in the graph is 25

Here, the edge between vertices representing Boulder and Colorado Springs has weight 25. But marking it would complete the circuit.

Hence, the edge between vertices representing Boulder and Colorado Springs is not marked...

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