---
tag: TMCVC2B092
kind: concept
name: Commuting graph
sources:
  - wikipedia: en:81460329@r1370333609
    locator: Commuting graph
    note: adopted
    mention: wikipedia://en/81460329
    sections: [Summary]
same_as:
  wikidata: Q137604228
  wikipedia: Commuting graph
inventory: [RXQB3Z7BHQ]
---

## Summary

In mathematics, the **commuting graph** of a [[semigroup|0XMEM406JM]], or in particular of a group, is an undirected graph in which the vertices are elements of the semigroup and there is an edge between any pair of elements that [[commute|099E72KTF8]] (that is, there is an edge between vertices $x$ and $y$ if and only if $xy=yx$ in the semigroup). Commuting graphs have been used to study groups and semigroups by seeking relationships between the combinatorial structure of the graph and the algebraic structure of the group or semigroup.