- Option $2$ explanation.
- A
- In this case, one component if complete subgraph and other one is an isolated vertex.
- Add two more edges to join the isolated vertex to the complete subgraph.
- We have one Hamiltonian cycles in this new graph

If Dirac's condition true then Then G is hamiltonian (regarding option 1)

If Ore's condition true then Then G is hamiltonian (regarding option 3)

If condition in option 2 is correct Then G is hamiltonian (regarding option 2)

**Will these three implications be true in opposite direction ??**