---
tag: FKN0M8SEQ3
kind: concept
name: Johnson graph
sources:
  - wikipedia: en:2948666@r1375553464
    locator: Johnson graph
    note: adopted
    mention: wikipedia://en/2948666
    sections: [Summary]
same_as:
  wikidata: Q6268493
  wikipedia: Johnson graph
inventory: [4KST5VFKBC]
---

## Summary

In mathematics, **Johnson graphs** are a special class of undirected graphs defined from systems of sets. The vertices of the Johnson graph $J(n,k)$ are the $k$-element [[subsets|0BJR9QR08E]] of an $n$-element set; two vertices are adjacent when the [[intersection|0ZNMMA9TF5]] of the two vertices (subsets) contains $(k-1)$-elements. Both Johnson graphs and the closely related Johnson scheme are named after Selmer M. Johnson.