Handshaking Lemma
The degree sum formula states that, given a graph ,
The formula implies that in any graph, the number of vertices with odd degree is even. This statement (as well as the degree sum formula) is known as the handshaking lemma. The latter name comes from a popular mathematical problem, to prove that in any group of people the number of people who have shaken hands with an odd number of other people from the group is even.
Read more about this topic: Degree (graph Theory)