Answer to Question #273570 in Discrete Mathematics for Asif

Question

3. Proof that an undirected graph has an even number of vertices of odd degree.

Answer 1

This sum must be even because the sum of the degrees of all vertices is equal to $2m$, where $m$ is a number of edges, and thus it is even, and the sum of the degrees of the vertices of even degrees is also even. Because this is the sum of the degrees of all vertices of odd degree in the graph, there must be an even number of such vertices.