Editing Degree (graph theory) (section)

==Handshaking lemma==
{{main|Handshaking lemma}}
The '''degree sum formula''' states that, given a graph <math>G=(V, E)</math>,

:<math>\sum_{v \in V} \deg(v) = 2|E|\, </math>.

The formula implies that in any undirected 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, which is 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.<ref>{{cite book
| last = Grossman | first = Peter
| title = Discrete Mathematics for Computing
| year = 2009
| url = https://books.google.com/books?id=K5lGEAAAQBAJ&pg=PA185
| page = 185
| publisher = [[Bloomsbury Publishing|Bloomsbury]]
| isbn = 978-0-230-21611-2
}}</ref>