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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.

1. P only
2. Q only
3. Both P and Q
4. Neither P nor Q

Correct answer: Both P and Q

Solution

In undirected graphs, the sum of the degrees of all vertices is always even because each edge contributes two to the total degree count. Additionally, the number of vertices with an odd degree must be even due to the Handshaking Lemma, which states that the sum of the degrees is equal to twice the number of edges.

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