   # Travel Use the edge-picking algorithm to design a route for the company representative in Exercise 19. ### 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 21ES
Textbook Problem
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## Travel Use the edge-picking algorithm to design a route for the company representative in Exercise 19.

To determine

To determine an efficient route for the representative to follow using the edge-picking algorithm.

### Explanation of Solution

Given information:

Given, a company representative lives in Louisville, Kentucky, and needs to visit offices in five different Indiana cities over the next few days.

The representative wants to drive between cities and return to Louisville at the end of the trip.

The estimated driving times, in hours, between cities are given in the table below:

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 1.3

Hence, the edge between vertices representing Bloomington and Indianapolis having the weight 1.3 is marked first.

The next least weight in the graph is 1.5

Hence, the edge between vertices representing Indianapolis and Lafayette having the weight 1.5 is marked.

The next least weight in the graph is 2.4

Here, the edge between vertices representing Bloomington and Lafayette has weight 2.4. But marking it would complete the circuit.

Hence, the edge between vertices representing Bloomington and Lafayette is not marked.

The next least weight in the graph is 3.0

Hence, the edge between vertices representing Fort Wayne and Lafayette having the weight 3...

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