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The sum of all the degrees is equal to twice the number of edges.

⇒ The sum of the degrees is even.
⇒ The sum of the degrees of vertices with even degree is even.
⇒ The sum of the degrees of vertices with odd degree must be even.

There must be an even number of vertices.

You must have asked this question under computer science section or there must be Data Structure and Algorithms section for such kind of questions.
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