---
tag: 7RXRXB3CTT
kind: concept
name: Moore graph
aliases: [moore-bound]
sources:
  - wikipedia: en:4112719@r1374109900
    locator: Moore graph
    note: adopted
    mention: wikipedia://en/4112719
    sections: [Summary]
same_as:
  wikidata: Q3115522
  wikipedia: Moore graph
inventory: [3FE0X5KB5K]
---

## Summary

In graph theory, a **Moore graph** is a [[regular graph|0KA4S8R39M]] whose girth (the shortest [[cycle|0Z05VCBQ7Y]] length) is more than twice its diameter (the distance between the farthest two vertices). If the [[degree|0KS0KRDV4Y]] of such a graph is $d$ and its diameter is $k$, its girth must equal $2k + 1$. This is true, for a graph of degree $d$ and diameter $k$, if and only if its number of vertices (its order) equals