Question

a) Prove that the number of vertices in a graph is always even.​

Answer 1

Answer:

Theorem: An undirected graph has an even number of vertices of odd degree. This sum must be even because 2m 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.

Answer 2

Step-by-step explanation:

The sum of degrees of any graph can be worked out by adding the degree of each vertex in the graph. The sum of degrees is twice the number of edges. Therefore, the sum of degrees is always even. Suppose e=0, then for any graph the number of odds vertices is even

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