Walks, trails, circuits, paths and cycles.

Which of the following is a Hamiltonian cycle of the graph?

• ABCDEFGA
• ACBEGFDA
• CBGEDFAC
• CEGBADFC

True or false: With Hamiltonian cycle, every edge must be crossed. With Euler circuits, every vertex must be crossed.

• True

• False

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

Euler trails must touch

• all edges
• all vertices

Which of the following is false?

• Euler trails 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 Trail.

• A graph with one odd vertex will have an Euler Trail but not an Euler Circuit.

Does this graph have a Hamiltonian Cycle, an Euler Circuit, both, or neither?

• Hamiltonian Cycle

• Euler Circuit

• Both

• Neither

Touching all vertices in a figure without repeating or picking up your pencil and starting and stopping at different spots

• Euler Circuit
• Euler Trail

• Hamiltonian Cycle

• Hamiltonian Path

Touching all vertices in a figure without repeating or picking up your pencil and starting and stopping at same spot

• Euler Circuit
• Euler Path
• Hamiltonian Cycle

• Hamiltonian Trail

Hamiltonian touches

• all edges
• all vertices