   # (a) determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why. (b)If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why. ### 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 21ES
Textbook Problem
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## (a) determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why. (b)If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why. To determine

To determine if the graph is Eulerian. If it is, to find an Euler circuit else to explain why not. And if the graph does not have an Euler circuit, to check if it has an Euler path. If it has to find it else to explain the reason for not having an Euler path.

### Explanation of Solution

Given information:

Given graph is

Calculation:

A graph is said to be Eulerian graph if it is a connected graph and every vertex of the graph has even degree.

Here,

The degree of A is 4

The degree of B is 4

The degree of C is 4

The degree of D is 4

The degree of E is 5

The degree of F is 5

The degree of G is 4

Since the graph is connected and all the vertices do not have even degree, the graph is not Eulerian.

A circuit (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)...

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