   # Transportation A subway map is shown below. Is it possible for a rider to travel the length of every subway route without repeating any segments? Justify your conclusion. ### 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 5.1, Problem 28ES
Textbook Problem
817 views

## Transportation A subway map is shown below. Is it possible for a rider to travel the length of every subway route without repeating any segments? Justify your conclusion. To determine

To determine if it is possible for a rider to travel the length of every subway route without repeating any segments.

### Explanation of Solution

Given information:

Given, a subway map below to check if it is possible for a rider to travel the length of every subway route without repeating any segments.

Calculation:

To check the possibility of the travel, the arrangement is to be graphed.

Every intersection is considered (since most of the subways are on single route) as a vertex and every route is considered an edge as shown below:

Using the above image, the graph can be made as:

It is possible for a rider to travel the length of every subway route without repeating any segments if the graph satisfies the condition of either Euler circuit or Euler path.

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. (i.e. no edge is used more than once).

Euler path is defined as the path in a connected graph that has exactly two vertices of odd degree with all the remaining vertices of even degree and the path starts at one of the vertices with odd degree and ends at the other vertex with odd degree...

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