An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and muomicronrhophiomegasigmaiotasigma (morphosis) "to form" or "to shape."

The automorphisms of a graph always describe a group (Skiena 1990, p. 19).

An automorphism of a region of the complex plane is a conformal self-map (Krantz 1999, p. 81).

See also

Anosov Automorphism, Field Automorphism, Graph Automorphism, Automorphism Group

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Krantz, S. G. Handbook of Complex Variables. Boston, MA: Birkhäuser, p. 81, 1999.Skiena, S. Implementing Discrete Mathematics: Combinatorics and Graph Theory with Mathematica. Reading, MA: Addison-Wesley, 1990.

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Cite this as:

Weisstein, Eric W. "Automorphism." From MathWorld--A Wolfram Web Resource.

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