Planar graphs, faces and Euler's formula v + f − e = 2

What this note covers

1. What planar means, and what it does not
2. Counting faces correctly
3. Euler's formula and how to apply it
4. Working from an incomplete picture
5. Where planar graphs turn up in practice
6. Setting out a planar-graph answer
7. How planar graph questions are examined and what separates a top answer

7 sections · 12 key terms & formulas · 6 common mistakes