GATE | GATE-CS-2001 | Question 50

How many undirected graphs (not necessarily connected) can be constructed out of a given set V = {v1, v2, … vn} of n vertices?
(A) n(n-1)/2
(B) 2n
(C) n!
(D) 2n(n-1)/2

Answer: (D)

Explanation: There are total n*(n-1)/2 possible edges. For every edge, there are to possible options, either we pick it or don’t pick. So total number of possible graphs is 2n(n-1)/2.

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