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 *2^n/2
(B) 2^n-2
(C) 2^n-3 *3
(D) 2^n-1


Answer: (C)

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

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