Find Hamiltonian circuits in the graphs below that have them

Find Hamiltonian circuits in the graphs below that have them. Explain why the other graphs do not.

Solution

A Hamilitonian circuit is one that visits every vertex exactly /only once.

(i) The first figure above is not hamiltonian circuit.

gbcdefa

This is is not ending with g again without visiting b again!. So this not hamiltonian circuit.

(ii) The second one is hamiltonian circuit because

gbcdefag.

Hence second figure has each vetrex is visited exactly once.