Question

Does the graph above have an Hamiltonian circuit, Hamiltonian path, or neither? Paths and Circuits Help

a. Only a Hamiltonian Path
b. It has both a Hamiltonian Path and Hamiltonian Circuit
c. It does not have either an Hamiltonian Path or an Hamiltonian Circuit​

Answer 1

a. Only a Hamiltonian path

One such path is

1 → 2 → 0 → 4 → 3

which satisfies the requirement that each vertex is visited exactly once.

There is no Hamiltonian circuit, however, since it is impossible for any Hamiltonian path on this graph to visit vertex 0 exactly once.