Consider the following. B E] X (a) Determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why.
Consider the following. B E] X (a) Determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Consider the following.
A
E
F
☆
B
(a) Determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why.
O Not Eulerian. There are vertices of degree less than four.
O Not Eulerian. There are vertices of odd degree.
O Not Eulerian. There are more than two vertices of odd degree.
Yes. E-A-D-E-G-D-C-G-F-C-B-F-A-B-E-F is an Euler circuit.
Yes. A-E-A-F-B-C-G-F-E-D-A-E is an Euler circuit.
(b) If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why.
O Yes. E-A-D-E-G-D-C-G-F-C-B-F-A-B-E-F is an Euler path.
O This graph does not have an Euler path. There are vertices of degree less than four.
O This graph does not have an Euler path. There are vertices of odd degree.
O The graph has an Euler circuit.
O This graph does not have an Euler path. There are more than two vertices of odd degree.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e099f26-ef4f-4e1b-ae39-eb9553e0b6b1%2F0fc15ad6-2f5d-44c5-8c41-5e6889566219%2Fg82hbh6_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the following.
A
E
F
☆
B
(a) Determine whether the graph is Eulerian. If it is, find an Euler circuit. If it is not, explain why.
O Not Eulerian. There are vertices of degree less than four.
O Not Eulerian. There are vertices of odd degree.
O Not Eulerian. There are more than two vertices of odd degree.
Yes. E-A-D-E-G-D-C-G-F-C-B-F-A-B-E-F is an Euler circuit.
Yes. A-E-A-F-B-C-G-F-E-D-A-E is an Euler circuit.
(b) If the graph does not have an Euler circuit, does it have an Euler path? If so, find one. If not, explain why.
O Yes. E-A-D-E-G-D-C-G-F-C-B-F-A-B-E-F is an Euler path.
O This graph does not have an Euler path. There are vertices of degree less than four.
O This graph does not have an Euler path. There are vertices of odd degree.
O The graph has an Euler circuit.
O This graph does not have an Euler path. There are more than two vertices of odd degree.
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