GATE | GATE-CS-2006 | Question 71

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 vertices of degree zero in G is:
(A) 1
(B) n
(C) n+1
(D) 2n


Answer: (C)

Explanation: There are n nodes which are single and 1 node which belong to empty set. And since they are not having 2 or more elements so they won’t be connected to anyone hence total number of nodes with degree 0 are n+1.

Thanks to roger for the explanation.

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