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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5, Problem 6T

Textbook Problem

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Low-Cost Route The table below shows the cost of direct train travel between various cities.

- Draw a weighted graph that represents the train fares.
- Use the edge-picking algorithm to find a route that begins in Angora, visits each city, and returns to Angora. What is the total cost of this route?
- Is it possible to travel along each train route and return to the starting city without traveling any routes more than once? Explain how you know.

To determine

**(b)**

**To find:**

Total cost of the route and design the route that begins with Angora.

**Given:**

The table shows the cost of direct rain travel between various cities.

**Calculation:**

Use edge picking algorithm to find a route that begins in Angora, visit each city and returns to Angora, That is find a Hamiltonian circuit

Step 1: Mark the edge of smallest weight in the graph (If two or more edge has the same weight, pick an one)

Step 2: Mark the edge of next smallest weight in the graph, as long as it does not complete a circuit and does not add a third marked edge t a single vertex

Step 3: Continue the process until one can no longer mark any edge...

To determine

**(c)**

**To justify:**

Possibility to travel along each train route and return to the starting route with traveling any route twice.

Mathematical Excursions (MindTap Course List)

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