   Chapter 10.1, Problem 10ES ### 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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# The solution for Example 10.1.6 shows a graph for which every vertex has even degree but which does not have an Euler circuit. Give another example of a graph satisfying these conditions.

To determine

The solution for Example 10.2.5 shows a graph for which every vertex has even degree but which does not have an Euler circuit. Give another example of a graph satisfying these properties.

Explanation

Given information:

The solution for Example 10.2.5 shows a graph for which every vertex has even degree but which does not have an Euler circuit.

Calculation:

DEFINITIONS:

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.

If G is a connected graph, then the graph cannot contain an Euler circuit as there dose not exist a walk between every pair of vertices (and thus no circuit either)...

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