In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem and uses a specified, set of generators for the group.
How do you make a Cayley graph?
Cayley Graphs
- Draw one vertex for every group element, generator or not. (And don't forget the identity!)
- For every generator aj, connect vertex g to gaj by a directed edge from g to gaj. Label this edge with the generator.
- Repeat step 2 for every element (i.e. vertex) g∈G.
Why are Cayley graphs important?
Cayley graphs give a way of encoding information about group in a graph. Given a group with a, typically finite, generating set, we can form a Cayley Graph for that group with respect to that generating set.
