A graph G with number of vertices greater and equal than three i.e. (n ≥ 3) is a Hamiltonian graph, if the degree of each vertex is greater and equal to _______________.

Correct option is C

For a graph to be Hamiltonian, each vertex must have a degree of at least half the number of vertices. This ensures sufficient connectivity for the existence of a Hamiltonian cycle.
Information Booster:
1. Hamiltonian Graph: A Hamiltonian graph is one that contains a Hamiltonian cycle, a cycle that visits every vertex exactly once.
2. Degree Condition: If the degree of each vertex is at least half the number of vertices, the graph is Hamiltonian by Dirac's Theorem.
Additional Knowledge:
· Eulerian Cycle vs. Hamiltonian Cycle: A graph with an Eulerian cycle visits every edge exactly once, whereas a Hamiltonian cycle visits every vertex once.
· Connectivity: This degree condition ensures that the graph is connected enough to allow a traversal of every vertex in a single cycle.