Which of the following statements is/are TRUE for an undirected graph?
P: The number of odd-degree vertices is even
Q: Sum of degrees of all vertices is even
(A)
P Only
(B)
Q Only
(C)
Both P and Q
(D)
Neither P nor Q
Answer: (C)
Explanation:
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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