Commuting graph

Summary

In mathematics, the commuting graph of a semigroup, 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 (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.