Handshaking lemma

Theorem (1.3) - Let $G=(V,E)$ be an undirected graph $|E|$ edges. Then $2|E|={\sum }_{v\in V}\text{deg}(v)$

Bipartite graph

${\sum }_{v\in A}\text{deg}(v)={\sum }_{v\in B}\text{deg}(v)=|E|$

Corollary

An undirected graph has an even number of vertices of odd degree. (Question 1)