Solution

The correct answer is Half of number of vertices

Key Points

• In graph theory, a graph G with n vertices (where \(n \geq 3\) ) is known to be Hamiltonian if it contains a Hamiltonian cycle, which is a cycle that visits every vertex exactly once and returns to the starting vertex.
• According to Dirac's theorem, a sufficient condition for a graph to be Hamiltonian is that the degree of each vertex is at least half of the number of vertices:

Correct Condition:

• Each vertex's degree \(\geq \frac{n}{2}\) , where n is the number of vertices.

Thus, the correct answer is: 3) Half of number of vertices