UGC-NET | UGC NET CS 2017 Jan – II | Question 5

Consider a Hamiltonian Graph G with no loops or parallel edges and with |V(G)| = n ≥ 3.
Then which of the following is true ?
(A) deg(v) ≥n/2 for each vertex v.
(B) |E(G)| ≥1/2(n – 1) (n – 2) + 2
(C) deg (v) + deg(w) ≥ n whenever v and w are not connected by an edge
(D) All of the above

Answer: (D)
Explanation:
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