Eulerian vs Hamiltonian graphs

A Hamiltonian cycle is

• A cycle that includes every vertex

• A cycle that includes every vertex more than once

• A cycle that includes every edge

• A cycle that includes every edge more than once

A Euler's or Hamiltonian Circuit end and start in the same place. 

• True
• False

In a Hamiltonian Path or Circuit, you must use each edge. 

• True 
• False

In a Hamiltonian Cycle or Path, you can only use each vertex once. 

• True
• False

In a Euler's Circuit or Path, you must use each edge once. 

• True
• False

In a Euler's Cycle or Path, you cannot use a vertex twice. 

• True
• False

Find a Hamilton Circuit starting at E. 

• E, A, C, D, B, E
• E, D, C, A, B, E
• E, D, C, B, A, E
• E, D, A, B, C, E

In a Hamiltonian Path, you must

• Travel every edge once and only once, returning to where you started

• Travel to every vertex once and only once, returning to where you started

• Travel every edge once and only once, not returning to where you started

• Travel to every vertex once and only once, not returning to where you started

The following is concerned with edges

• Hamiltonian

• Eulerian

What is a quick hint to determining an Eulerian graph