GATE | GATE-CS-2006 | Question 73

The 2n vertices of a graph G corresponds to all subsets of a set of size n, for n >= 6. Two vertices of G are adjacent if and only if the corresponding sets intersect in exactly two elements.

The number of connected components in G is:
(A) n
(B) n+2
(C) 2n/2
(D) 2n / n


Answer: (B)

Explanation: n+1 nodes of the graph not connected to anyone as explained in question 70 while others are connected so total number of connected components are n+2 (n+1 connected components by each of the n+1 vertices plus 1 connected component by remaining vertices).

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