In an Hamiltonian Graph (G) with no loops and parallel edges:
According to Dirac's theorem in a n vertex graph, deg (v) ≥ n / 2 for each vertex of G.
According to Ore's theorem deg (v) + deg (w) ≥ n for every n and v not connected by an edge is sufficient condition for a graph to be hamiltonian.
If |E(G)| ≥ 1 / 2 * [(n - 1) (n - 2)] then graph is connected but it doesn't guaranteed to be Hamiltonian Graph.
(a) and (c) is correct regarding to Hamiltonian Graph.
So, option (C) is correct.
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