Corollary 3.1

In any graph, the number of vertices of odd degree is even

Proof

Let $x_1\dots ,x_n$ be vertices of graph $G$ with even degree and let $y_1,\dots ,y_m$ be vertices of odd degree
Let $S=d(x_1)+\cdots +d(x_n)$
and $T=d(y_1)+\cdots +d(y_m)$
By Theorem 3.1, $S+T$ is even
Since $S$ is the sum of even numbers, $S$ is even
So $T$ must be even
Since $T$ is the sum of $m$ odd numbers, $m$ must be even