---
tag: JAK0VB4J70
kind: concept
name: Vertex separator
aliases: [vertex-cut]
sources:
  - wikipedia: en:1499165@r1376212721
    locator: Vertex separator
    note: adopted
    mention: wikipedia://en/1499165
    sections: [Summary]
same_as:
  wikidata: Q7922780
  wikipedia: Vertex separator
inventory: [8769Z67Q8T]
---

## Summary

In graph theory, a vertex [[subset|0BJR9QR08E]] $S \subset V$ is a **vertex separator** (or **vertex cut**, or **separating set**) for nonadjacent vertices $a$ and $b$ if the removal of $S$ from the [[graph|00C0BR7D7H]] separates $a$ and $b$ into distinct connected components.