How many undirected graphs (not necessarily connected) can be constructed out of a given set V= {V 1, V 2,…V n} of n vertices ?
(A) n(n-l)/2
(B) 2^n
(C) n!
(D) 2^(n(n-1)/2)
Answer: (D)
Explanation: In an undirected graph, there can be maximum n(n-1)/2 edges. We can choose to have (or not have) any of the n(n-1)/2 edges. So, total number of undirected graphs with n vertices is 2^(n(n-1)/2).
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