Schreier coset graph
The edges of the graph are of the form (Hg,Hgxi).
The book "Categories and Groupoids" listed below relates this to the theory of covering morphisms of groupoids. A subgroup H of a group G determines a covering morphism of groupoids and if X is a generating set for G then its inverse image under p is the Schreier graph of (G,X).
The graph is named after Otto Schreier.
Coset graphs can be used to form large permutation representations of groups and were used by Graham Higman to show that the alternating groups of large enough degree are Hurwitz groups, (Conder 2003).
Every vertex-transitive graph is a coset graph.
- Conder, Marston (2003), "Group actions on graphs, maps and surfaces with maximum symmetry", Groups St. Andrews 2001 in Oxford. Vol. I, London Math. Soc. Lecture Note Ser. 304, Cambridge University Press, pp. 63–91, MR 2051519
- Gross, Jonathan L.; Tucker, Thomas W. (1987), Topological graph theory, Wiley-Interscience Series in Discrete Mathematics and Optimization, New York: John Wiley & Sons, ISBN 978-0-471-04926-5, MR 898434
- Schreier graphs of the Basilica group Authors: Daniele D'Angeli, Alfredo Donno, Michel Matter, Tatiana Nagnibeda
- Philip J. Higgins, Categories and Groupoids, van Nostrand, New York, Lecture Notes, 1971, Republished as TAC Reprint, 2005
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