Let \(G=(V,E,\gamma)\) be an undirected graph, \(v\in V\) be a vertex of \(G\). The number of edges incident to \(v\) is called the degree of \(v\) and denoted by \(\deg_G(v)\). Formally, we set \[\deg_G(v):=|\delta_G(v)|\] with \(\delta_G(v)=\{e\in E: v\in \gamma(e)\}\). Note that the index \(G\) can be omitted in the notation, if it is clear from the context, which graph \(G\) is concerned.
The values of the degrees of vertices in the above graph are:
| Vertex \(v\) | Degree \(\deg(v)\) |
|---|---|
| \(a\) | \(5\) |
| \(b\) | \(6\) |
| \(c\) | \(4\) |
| \(d\) | \(3\) |
| \(e\) | \(4\) |
| \(f\) | \(0\) |
Corollaries: 1
Definitions: 2 3 4 5 6
Explanations: 7
Lemmas: 8 9 10
Proofs: 11 12 13 14 15 16 17 18 19 20 21 22
Propositions: 23 24
Theorems: 25 26 27
