How should I show the following:
If a graph has order $99$ , then show that it has a vertex of even degree.
I don't get how to prove it, maybe we need the use of fact that the sum of all degrees in graph has to be even..
Kindly help..
2026-05-14 22:52:01.1778799121
If a graph has order 99 then it has a vertex of even degree .
181 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail At
1
The number of vertices of odd degree is even in any finite simple graph.This is because the sum of the degrees of the vertices is twice the number of edges(hence even). Since this sum is even there is an even number of vertices of odd degree.If there is an even number of vertices of odd degree and $99$ vertices we conclude there is an odd number of vertices of even degree. Because of this there is at least one.