# Transportation For the direct air flights given in Exercise 2, is it possible to start at one city and fly every route offered without repeating any flight if you return to the starting city? Explain how you reached your conclusion.

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

Chapter
Section

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 5.1, Problem 26ES
Textbook Problem
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## Transportation For the direct air flights given in Exercise 2, is it possible to start at one city and fly every route offered without repeating any flight if you return to the starting city? Explain how you reached your conclusion.

To determine

To determine if it is possible to start at one city and fly every route offered without repeating any flight if the end point is same as the starting city.

### Explanation of Solution

Given information:

Given, the table below shows the nonstop flights offered by a small airline.

A graph is to be made where each vertex represents a city and an edge connects two vertices if there is a nonstop flight between the corresponding cities.

â€ƒâ€ƒ

And the graph is,

â€ƒâ€ƒ

Calculation:

It is possible to start at one city and fly every route offered without repeating any flight and end point is same as the starting city if the graph satisfies the condition of either Euler circuit.

An Eulerian graph (that starts and ends at the same vertex) is said to be Euler circuit if it uses every edge, but only once...

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