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Q4C. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} Explain why the graph either does or does not have an Euler circuit. a C d g Two vertices (b and f) have odd degree. Therefore, the graph does not have an Euler circuit. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have even degree. Therefore, the graph does have an Euler circuit.

Q4C. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} Explain why the graph either does or does not have an Euler circuit. a C d g Two vertices (b and f) have odd degree. Therefore, the graph does not have an Euler circuit. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have even degree. Therefore, the graph does have an Euler circuit.

Holt Mcdougal Larson Pre-algebra: Student Edition 2012
Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter12: Angle Relationships And Transformations
Section12.5: Reflections And Symmetry
Problem 20E
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Q4C. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} Explain why the graph either does or does not have an Euler circuit. b a d e g Two vertices (b and f) have odd degree. Therefore, the graph does not have an Euler circuit. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have even degree. Therefore, the graph does have an Euler circuit.
Transcribed Image Text:Q4C. Consider the graph with the following vertices and edges: V = {a, b, c, d, e, f, g} E = {{a, b}, {a, c}, {a, f}, {b, c}, {b, f}, {c, d}, {c, g}, {d, e}, {d, f}, {f, g}} Explain why the graph either does or does not have an Euler circuit. b a d e g Two vertices (b and f) have odd degree. Therefore, the graph does not have an Euler circuit. Four vertices (a, b, d, and e) have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have odd degree. Therefore, the graph does not have an Euler circuit. All vertices have even degree. Therefore, the graph does have an Euler circuit.
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