Q5B. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, f}, {d, e}, {d, f}} Explain why the graph either does or does not have an Euler trail. C b A f a d CD All vertices have even 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 odd degree. Therefore, the graph does not have an Euler trail. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not hav an Euler trail.
Q5B. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, f}, {d, e}, {d, f}} Explain why the graph either does or does not have an Euler trail. C b A f a d CD All vertices have even 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 odd degree. Therefore, the graph does not have an Euler trail. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not hav an Euler trail.
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

Transcribed Image Text:Q5B. Consider the graph with the following vertices and edges:
V = {a, b, c, d, e, f}
E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, f}, {d, e}, {d, f}}
Explain why the graph either does or does not have an Euler trail.
C
b
a
f
d
e
CD
All vertices have even 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 odd degree. Therefore, the graph does not have an Euler trail.
Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have
an Euler trail.
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