Data Structures | Graph | Question 2

The degree sequence of a simple graph is the sequence of the degrees of the nodes in the graph in decreasing order. Which of the following sequences can not be the degree sequence of any graph? 

I. 7, 6, 5, 4, 4, 3, 2, 1
II. 6, 6, 6, 6, 3, 3, 2, 2
III. 7, 6, 6, 4, 4, 3, 2, 2
IV. 8, 7, 7, 6, 4, 2, 1, 1 

(A)

I and II

(B)

III and IV

(C)

IV only

(D)

II and IV

Answer: (D)

Explanation:

Both II and IV cannot be the degree sequence of any graph.

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