Question

Prove that in any graph .There are an every number of Vertices of odd degree​

Answer 1

Every number of Vertices of odd degree must be even

Explanation:

• Each edge is linked with two vertices — no edges to anywhere.  
• Hence the cumulative degrees of all vertices have to be even.
• The number of odd-degree vertices must be odd or even because it is a set's cardinal that must be non-negative.
• If there are an odd number of odd degree vertices in the graph, the sum of all vertex degrees in the graph will be odd, but this is not allowed by 2, so that condition must never occur.
• So there has to be an even number of odd degree vertices.