Question

PLEASE ANSWER IN CLEAR PRINT, NOT CURSIVE- PLEASE WRITE CLEARLY

1. What is the difference between a Eulerian Path and Circuit?
2. What is the difference between a Hamiltonian Path and Circuit?
3. Is the image below Eulerian or Hamiltonian, Path or Circuit?
4. How did you determine your answer?

Answer 1

(1) An Eulerian path is a path that uses every edge in a graph with no repeats. Being a path, it doesnot have to return to the starting vertex whereas an Eulerian circuit is a circuit that uses every edge in a graph with no repeats. Being a circuit, it must start and end at the same vertex.

(2) A Hamiltonian circuit is a circuit that visits every vertex once with no repeats. Being a circuit, it must start and end at the same vertex whereas a Hamiltonian path also visits every vertex once with no repeats, but does not have to start and end at the same vertex.

(3) The given figure is a Hamiltonian circuit because it visits every vertices at once and it start and end with same vertex. It is not Eulerian because it doesn't cover all the edges.