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Consider a Hamiltonian Graph G with no loops or parallel edges and with $|V(G)| = n ≥ 3$. Then which of the following is true ?

(1) $deg(v) ≥ \frac{n}{2}$ for each vertex v.

(2) $|E(G)| ≥ \frac{1}{2}(n – 1) (n – 2) + 2$

(3) $deg (v) + deg(w) ≥ n$ whenever v and w are not connected by an edge.

(4) All of the above
asked in Graph Theory by Loyal (4.3k points)
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