---
tag: CG91WNMG2T
kind: concept
name: Graph embedding
msc: [05C10, 57M15]
sources:
  - url: https://en.wikipedia.org/wiki/Graph_embedding
same_as:
  wikidata: Q5597085
  wikipedia: Graph embedding
---

## Summary

An embedding of a graph in a surface is a drawing of the graph on the surface in which edges meet only at shared ends.
Embeddings in the plane or sphere are the subject of planar graph theory, and embeddings in other surfaces lead to the genus of a graph.
Many results, such as [[Euler's formula|0W1C598HMS]] and the notion of a [[dual graph|1QHTD1DS5J]], are statements about embedded graphs.

## Explanations

### L1 human

To embed a graph is to draw it on a surface with no two edges crossing.
Some graphs, like $K_5$, cannot be drawn on a sheet of paper without crossings, but they can be drawn on the surface of a doughnut.
The genus of a graph measures how many handles a surface needs before the graph fits on it.