---
tag: X7W1JX98Z9
kind: concept
name: Hamming graph
sources:
  - wikipedia: en:8046549@r1317745629
    locator: Hamming graph
    note: adopted
    mention: wikipedia://en/8046549
    sections: [Summary]
same_as:
  wikidata: Q369440
  wikipedia: Hamming graph
inventory: [156WJ7MRG3]
---

## Summary

**Hamming graphs** are a special class of [[graphs|00C0BR7D7H]] named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let $S$ be a [[set|0BSJ7RQ9BW]] of $q$ elements and $d$ a positive [[integer|0C4JS9RF5M]]. The Hamming graph $H(d,q)$ has vertex set $S^{d}$, the set of ordered $d$-[[tuples|9HFER6N708]] of elements of $S$, or sequences of length $d$ from $S$. Two vertices are [[adjacent|00C0BR7D7H]] if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph $H(d,q)$ is, equivalently, the Cartesian product of $d$ [[complete graphs|03WKB2H474]] $K_{q}$.