Handshake Lemma/Corollary

Corollary to the Handshake Lemma
Let $G$ be a $\left({p, q}\right)$-graph, which may be a multigraph or a loop-graph, or both.

The number of odd vertices in $G$ must be even.

Proof
From the Handshake Lemma, the sum of all the degrees of all the vertices of a graph is equal to twice the total number of its edges.

The result follows from the fact that the sum of an odd number of odd numbers is itself odd.