When a group is mapped to itself it is called an automorphism, and for topological spaces it is called a homeomorphism.
Finding this property in graphs is an interesting problem in computer science since it has not been proven to be in either the class P or NP- Complete. A space of this type is one where both addition and scalar multiplication are preserved, and for a group, all identities and inverses of the group are preserved. When a group is mapped to itself it is called an automorphism, and for topological spaces it is called a homeomorphism. Formally defined as a morphism which is bijective, this is, FTP, what type of mapping which preserves sets and relations among elements?
Finding this property in graphs is an interesting problem in computer science since it has not been proven to be in either the class P or NP- Complete.
isomorphism