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Needed a Document for isomorphism and automorphism? Related: Element...
Generally an automorphism is a special case of isomorphism when an entity is mapped to itself. So, for example, a field automorphism is an isomorphism of the field with itself. It's not surprising that such a thing exists, since the identity map is one such isomorphism, but there are often additional automorphisms (and the automorphisms of an entity form a group under function composition).

Regarding graphs specifically, one again has the sense that automorphism means an isomorphism of a graph with itself. But there is something to note here. We sometimes consider graphs with vertices "labelled" and sometimes without labelling the vertices. In the latter case we are considering graphs as distinct only "up to isomorphism".

Thus to talk about automorphisms of graphs we necessarily would consider the vertices to be labelled, because otherwise (with unlabelled vertices) the notion of automorphism would be trivial (per the identity map as mentioned above).
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Needed a Document for isomorphism and automorphism? Related: Elementary Set Theory - CSIR-NET Mathematical Sciences?
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Needed a Document for isomorphism and automorphism? Related: Elementary Set Theory - CSIR-NET Mathematical Sciences? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about Needed a Document for isomorphism and automorphism? Related: Elementary Set Theory - CSIR-NET Mathematical Sciences? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Needed a Document for isomorphism and automorphism? Related: Elementary Set Theory - CSIR-NET Mathematical Sciences?.
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