4 Determine whether each of the following graphs has a Hamil

4. Determine whether each of the following graphs has a Hamiltonian circuit. If it does have an Hamiltonian circuit, find such a circuit. If it does not have an Hamiltonian circuit, explain why you can be 100% sure that it does not.

Solution

A Hamilton path is such that there is an edge in the graph from the first vertex of the graph to the last vertex of the graph.

Hamiltonian path exists in the curve but there doesn\'t exists any hamiltonian cycle, hamiltonian path exists in the first graph

a,b,h,c,g,f,e,h

since there are odd cycles loop in the curve there can\'t be any hamiltonian cycle in the first graph.

The second graph contains also odd loop curves in the graph hence hamiltonian cycle doesn\'t exists in this graph