GATE | GATE-CS-2009 | Question 3

Which one of the following is TRUE for any simple connected undirected graph with more than 2 vertices?
(A) No two vertices have the same degree.
(B) At least two vertices have the same degree.
(C) At least three vertices have the same degree.
(D) All vertices have the same degree.


Answer: (B)

Explanation: Since the graph is simple, there must not be any self loop and parallel edges.

Since the graph is connected, the degree of any vertex cannot be 0.

Therefore, degree of all vertices should be be from 1 to n-1. So the degree of at least two vertices must be same.

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