Unit 4 - Graph Theory Review

Tracing all edges on a figure without picking up your pencil or repeating and starting and stopping at different spots

• Euler Circuit
• Euler Path

Tracing all edges on a figure without picking up your pencil and repeating and starting and stopping in the same spot

• Euler Circuit
• Euler Path

Circuits start and stop at 

• same vertex
• different vertices

Paths start and stop at

• same vertex
• different vertices

Euler paths must touch

• all edges
• all vertices

Which of the following is false?

• Euler Paths exist when there are exactly two vertices of odd degree.
• Euler circuits exist when the degree of all vertices are even.
• A graph with more than two odd vertices will never have an Euler Path or Circuit.
• A graph with one odd vertex will have an Euler Path but not an Euler Circuit.

Does this graph have an Euler Path, Euler Circuit, both, or neither?

• Euler Path
• Euler Circuit
• Both
• Neither

This graph will have a Euler's Path. 

• True
• False

This graph will have a Euler's Circuit

• True
• False

Identify the Euler's Circuit

• KLQPQOKLOMK
• KLQMPQOKNLOMK
• KLQMPQOK
• KMOLNKOQMK