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MathidiaMathematics Academy
Graph theory
Lesson 8 of 10
Introduction

Degrees and the handshaking lemma

Objective. Use the handshaking lemma to relate degrees and edges.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: 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?

3 … 3
Coordinate grid with the line 3 … 3
  1. 1Sum of degrees: 3 + 3 + 2 + 2 = 10.
  2. 2Edges = 10 ÷ 2.

Answer: 5 edges

Concept mastery

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Practice

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Common mistake. Counting each edge once when summing degrees.

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