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Consider the following set : {1,2,3,.....n}. Now consider all possible subset. Two subset S1 and S2 are having edge between them only if their intersection has two common elements.

a) Number of isolated vertices.
b) Number of components
c) Highest degree possible.


a) n+1
b) n+2
c) 3*2n-3

I have problem in c) part answer.
My answer is 2n - n - 2
My Approach:
I believe Highest degree should be of subset: {1,2,3....n} itself.
as it will be connected to every other vertices across.
It only not connected with single element set, phi and itself.
So its degree is 2n - n - 2 which must be highest.
Please suggest suitable approach to it.

closed as a duplicate of: GATE2006-71
asked in Graph Theory by Active (1.6k points) 16 47 71
retagged by | 132 views

1 Answer

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Your solution seems correct. But

"intersection has two common elements"

Is it exactly two or at least two?
answered by Veteran (319k points) 577 1445 2962

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