PLEASE ANSWER IN CLEAR PRINT, NOT CURSIVE- PLEASE WRITE CLEARLY What is the difference between a...
PLEASE ANSWER IN CLEAR PRINT, NOT CURSIVE- PLEASE WRITE CLEARLY
- What is the difference between a Eulerian Path and Circuit?
- What is the difference between a Hamiltonian Path and Circuit?
- Is the image below Eulerian or Hamiltonian, Path or Circuit?
- How did you determine your answer?
Homework Answers
(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.
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