State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an
Euler circuit, find one.
A)neither
B)Euler path: H, C, A, B, C, D, E, F, D, G, H, G
C)Euler circuit: A, B, C, D, E, F, D, G, H, C, A
D)Euler path: H, C, A, B, C, D, E, F, D, G

Question

State whether the graph has an Euler path, an Euler circuit, or neither. If it has an Euler path or an
Euler circuit, find one. 
A)neither 
B)Euler path: H, C, A, B, C, D, E, F, D, G, H, G 
C)Euler circuit: A, B, C, D, E, F, D, G, H, C, A 
D)Euler path: H, C, A, B, C, D, E, F, D, G

Quizplus · Accepted Answer

The graph has odd degree vertices (H, G, F) which means it cannot have an Euler circuit. However, it does have an Euler path that starts and ends at vertex H, which is provided in choice B. Choices C and D incorrectly state that the graph has an Euler circuit. Choice A correctly states that the graph has neither an Euler path nor an Euler circuit. The graph has an Euler path, as shown in option B. It starts and ends at vertex H and visits every edge exactly once. The other options either incorrectly state that there is an Euler circuit when there is not (option C) or omit part of the path (option D) or falsely claim that there is neither an Euler path nor an Euler circuit (option A).

State Whether the Graph Has an Euler Path, an Euler