Explain why the graph either does or does not have an Euler trail. C b a f d e

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.5: The Format Proof Of A Theorem
Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...
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Explain why the graph either does or does not have an Euler trail.
C
b
a
d
e
CD
Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have
an Euler trail.
Exactly two vertices (c and e) have odd degree. Therefore, the graph does have
an Euler trail.
Exactly two vertices (b and e) have odd degree. Therefore, the graph does have
an Euler trail.
All vertices have even degree. Therefore, the graph does not have an Euler trail.
All vertices have odd degree. Therefore, the graph does not have an Euler trail.
Transcribed Image Text:Explain why the graph either does or does not have an Euler trail. C b a d e CD Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler trail. Exactly two vertices (c and e) have odd degree. Therefore, the graph does have an Euler trail. Exactly two vertices (b and e) have odd degree. Therefore, the graph does have an Euler trail. All vertices have even degree. Therefore, the graph does not have an Euler trail. All vertices have odd degree. Therefore, the graph does not have an Euler trail.
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