---
tag: 3D7M2QFBG6
kind: concept
name: Grassmann graph
sources:
  - wikipedia: en:54639900@r1301284437
    locator: Grassmann graph
    note: adopted
    mention: wikipedia://en/54639900
    sections: [Summary]
same_as:
  wikidata: Q85867362
  wikipedia: Grassmann graph
inventory: [VC4EVCBFQG]
---

## Summary

In graph theory, **Grassmann graphs** are a special class of simple graphs defined from systems of [[subspaces|00YC1D652K]]. The vertices of the Grassmann graph $J_{q}(n, k)$ are the $k$-dimensional subspaces of an $n$-dimensional [[vector space|000AYPA9AJ]] over a [[finite field|0ZXZ82FTX2]] of order $q$; two vertices are adjacent when their [[intersection|0ZNMMA9TF5]] is $(k - 1)$-dimensional.