Graph theory
Lesson 8 of 10
Degrees and the handshaking lemma
Objective. Use the handshaking lemma to relate degrees and edges.
The key idea
Each edge contributes 1 to the degree of two vertices, so the sum of all degrees equals twice the number of edges — and is always even.
Worked example
A graph has degrees 3, 3, 2, 2. How many edges?
- 1Sum of degrees: 3 + 3 + 2 + 2 = 10.
- 2Edges = 10 ÷ 2.
Answer: 5 edges
Practice
Each question comes with a picture and a listen button. Try it first, then reveal the answer.
Common mistake. Counting each edge once when summing degrees.
Your progress
Tick each step as you finish it — Continue brings you back here.
0 of 5 steps complete