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4th Edition

Richard N. Aufmann + 3 others

Publisher: Cengage Learning

ISBN: 9781305965584

Chapter 5.1, Problem 16ES

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.

**Given information:**

Given graph is

â€ƒâ€ƒ

**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 3

The degree of B is 4

The degree of C is 2

The degree of D is 2

The degree of E is 3

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).

Since the graph is not Eulerian, Euler circuit does not exist...

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