# GATE | GATE-CS-2014-(Set-1) | Question 62

An ordered n-tuple (d1, d2, … , dn) with d1 >= d2 >= ⋯ >= dn is called graphic if there exists a simple undirected graph with n vertices having degrees d1, d2, … , dn respectively. Which of the following 6-tuples is NOT graphic?

**(A)** (1, 1, 1, 1, 1, 1)

**(B)** (2, 2, 2, 2, 2, 2)

**(C)** (3, 3, 3, 1, 0, 0)

**(D)** (3, 2, 1, 1, 1, 0)

**Answer:** **(C)** **Explanation:** The required graph is not possible with the given degree set of (3, 3, 3, 1, 0, 0). Using this 6-tuple the graph formed will be a Disjoint undirected graph, where the two vertices of the graph should not be connected to any other vertex ( i.e. degree will be 0 for both the vertices ) of the graph. And for the remaining 4 vertices the graph need to satisfy the degrees of (3, 3, 3, 1).

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