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A **Cayley graph** is a graphical representation of a group that illustrates the structure and properties of the group in terms of its generators. Named after the mathematician Arthur Cayley, this type of graph provides a way to visualize how elements of a group can be combined (or multiplied) to produce other elements.

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  1. Cayley graphs
  2. Algebraic graph theory
  3. Algebra
  4. Fields of mathematics
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Cayley graph by Ciro Santilli 37 Updated 2025-06-17 +Created 1970-01-01
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You select a generating set of a group, and then you name every node with them, and you specify:
  • each node by a product of generators
  • each edge by what happens when you apply a generator to each element
Not unique: different generating sets lead to different graphs, see e.g. two possible en.wikipedia.org/w/index.php?title=Cayley_graph&oldid=1028775401#Examples for the
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