Graph Theory

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

• Euler Circuit

• Euler Path

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

• Euler Circuit

• Euler Path

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 Circuit

• True
• False

Identify the Euler's Circuit

• KLQPQOKLOMK
• KLQMPQOKNLOMK
• KLQMPQOK
• KMOLNKOQMK

Is the following graph complete?

• Yes

• No

Is the following graph complete?

• Yes

• No

Is the following graph connected?

• Yes

• No