---
tag: 5Y3AV07EDV
kind: concept
name: Apex graph
sources:
  - wikipedia: en:28228942@r1350035304
    locator: Apex graph
    note: adopted
    mention: wikipedia://en/28228942
    sections: [Summary]
same_as:
  wikidata: Q4779442
  wikipedia: Apex graph
inventory: [N9RVT0ZBAD]
---

## Summary

In graph theory, a branch of mathematics, an **apex graph** is a [[graph|00C0BR7D7H]] that can be made [[planar|029JQEK15B]] by the removal of a single vertex. The deleted vertex is called an apex of the graph. It is *an* apex, not *the* apex because an apex graph may have more than one apex; for example, in the minimal nonplanar graphs $K_{5}$ or $K_{3,3}$, every vertex is an apex. The apex graphs include graphs that are themselves planar, in which case again every vertex is an apex. The null graph is also counted as an apex graph even though it has no vertex to remove.