Graph Theory

Hamiltonian and Euler cycles must have verticies of ___ degree.

What is the name for a cycle that passes through each vertex only once, except for the starting and ending points?

• cycle

• Euler cycle

• Hamiltonian Cycle

What is the name for a cycle that passes through each edge only once, except for the starting and ending points?

• cycle

• path

• Euler cycle

• Hamiltonian cycle

In Euler and Hamiltonian cycles, you must touch all the ___ in the graphs.

• verticies

• edges

• verticies and edges

Can you find an Euler cycle in the following graph?

• Yes

• No

Are the graphs isomorphic?

• Yes

• No

Are the graphs isomorphic?

• Yes

• No

Are the graphs isomorphic?

• Yes

• No

What is the ONE difference between a Hamiltonian cycle and the TSP?

Give (if any) a possible Hamiltonian cycle in the graph.