Schreier coset graph

Summary

Let $G$ be a group, $H$ a subgroup and $S$ a set of elements of $G$. The Schreier coset graph is a directed graph whose vertices are the right cosets of $H$, with an edge labelled $s$ from $Hg$ to $Hgs$. For $H = \set{1}$ it is the Cayley graph of $G$ with respect to $S$. It shows how the generators permute the cosets of $H$. It is used in coset enumeration and to find generators of subgroups, as in the Reidemeister–Schreier method.