I know that degree of a vertex of an (undirected) graph is the number of edges incident to the vertex. I need to prove that in an arbitrary graph the number of vertices with odd degree is even. How to formally prove it?
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1Hint : Hand-shake lemma – Peter Dec 08 '20 at 13:09
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1See this. – David Mitra Dec 08 '20 at 13:10
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The sum of degrees of all vertices is even. Thus the number of odd-degree vertices must be even, since otherwise the first sum is odd (even-degree vertices do not affect the parity of the first sum).
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