---
tag: VG7DWJBYB9
kind: concept
name: Hypercube graph
aliases: [cube-graph, q-n]
sources:
  - wikipedia: en:6706815@r1366110735
    locator: Hypercube graph
    note: adopted
    mention: wikipedia://en/6706815
    sections: [Summary]
same_as:
  wikidata: Q958394
  wikipedia: Hypercube graph
inventory: [60CKR6TEK8]
---

## Summary

In graph theory, the **hypercube graph** $Q_n$ is the edge graph of the $n$-dimensional hypercube, that is, it is the graph formed from the vertices and edges of the hypercube. For instance, the cube graph $Q_3$ is the graph formed by the 8 vertices and 12 edges of a three-dimensional cube. $Q_n$ has $2^n$ vertices, $2^{n-1}n$ edges, and is a [[regular graph|0KA4S8R39M]] with $n$ edges touching each vertex.