GATE | GATE-CS-2006 | Question 72

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 maximum degree of a vertex in G is:
(A) (n/2)C2 *2n/2
(B) 2n-2
(C) 2n-3 *3
(D) 2n-1

Answer: (C)

Explanation: maxk(kC2*2(n−k))=3C2*2(n−3)=3*2(n−3).

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