   Chapter 10.1, Problem 11ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Is it possible for a citizen of Königsberg to make a tour of the city and cross each bridge exactly twice? (See Figure 10.1.1.) Explain.

To determine

Is it possible for a citizen of Konigsberg to make a tour of the city and cross every bridge exactly twice? Why?

Explanation

Given information:

Calculation:

An Euler circuit is a circuit that contains every edge of the graph.

A connected graph has an Euler circuit if and only if each of the vertices has an even degree.

Let us first create a graph that corresponds with the given figure. Each region is represented by a vertex and each bridge between two regions is represented by an edge between two corresponding vertices.

We then obtain the following graph.

We need to cross each bridge exactly twice...

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