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handshaking lemma


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The simple result that, in any graph, the sum of the degrees of all the vertices is even. (The name arises from its application to the total number of hands shaken when some members of a group of people shake hands.) It follows from the simple observation that the sum of the degrees of all the vertices of a graph is equal to twice the number of edges. A result which follows from it is that, in any graph, the number of vertices of odd degree is even.

Subjects: Mathematics.


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