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GATE | GATE CS 2013 | Question 25

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Which of the following statements is/are TRUE for undirected graphs? 

P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even. 



Neither P nor Q


Both P and Q


Q only


P only

Answer: (B)


P is true: For undirected graph as adding an edge always increases degree of two vertices by 1.

Q is true: If we consider sum of degrees and subtract all even degrees, we get an even number because every edge increases the sum of degrees by 2. So total number of odd degree vertices must be even.

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Last Updated : 28 Jun, 2021
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