Cayley graph

The Cayley graph of the free group on two generators a and b
Graph families defined by their automorphisms
distance-transitive distance-regular strongly regular
symmetric (arc-transitive) t-transitive, t ≥ 2 skew-symmetric
(if connected)
vertex- and edge-transitive
edge-transitive and regular edge-transitive
vertex-transitive regular (if bipartite)
biregular
Cayley graph zero-symmetric asymmetric

In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group,[1] is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central tool in combinatorial and geometric group theory. The structure and symmetry of Cayley graphs makes them particularly good candidates for constructing expander graphs.

  1. ^ Magnus, Wilhelm; Karrass, Abraham; Solitar, Donald (2004) [1966]. Combinatorial Group Theory: Presentations of Groups in Terms of Generators and Relations. Courier. ISBN 978-0-486-43830-6.