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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
This can be solved using havel hakimi theorem, which says :
So, we check each degree sequence given in question :
Since (I) comes only in one option i.e. option (A), it is correct answer. We don't need to check for other sequences.
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
This can be solved using havel hakimi theorem, which says :
So, we check each degree sequence given in question :
Since (I) comes only in one option i.e. option (A), it is correct answer. We don't need to check for other sequences.