Network in Graph Theory
Degree of a vertex
The number of edges meeting at a vertex.
| English | Degree of a vertex |
|---|---|
| Bahasa Melayu | Darjah bucu |
| 中文 | 顶点的度 |
How it is used
A vertex D has edges to A, B, C and E, so the degree of D is 4. A vertex with no edges has degree 0 and is called isolated; a vertex on the end of a single path has degree 1.
Where it shows up in SPM
Appears in the Network in Graph Theory chapter (Form 5). Paper 1 asks for the degree of a stated vertex from a diagram; Paper 2 combines degrees with the rule that their sum is twice the number of edges to solve for an unknown number of edges or vertices.
Don't confuse it with
Open the chapter: Network in Graph Theory →
Frequently asked questions
What is an isolated vertex?
An isolated vertex is a point with no edges attached, so its degree is 0. It is part of the network's list of vertices but is not connected to any other vertex, like a town with no roads reaching it.
If I know all the degrees, how do I find the number of edges?
Add up every vertex's degree, then divide the total by 2, because each edge is counted twice, once at each end. For degrees 4, 3, 3 and 2 the sum is 12, so the number of edges is 12 ÷ 2 = 6.