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A permutation p of the vertex set of a graph G with the property that {a,b} is an edge if and only if {p(a), p(b)} is an dege, is called an automorphism of G. Is this right? this sounds isomorphism to me.
An automorphism is a transformation that preserves the structure of an object or system. In other words, it is a function that maps an object or system onto itself, while maintaining its characteristics and relationships.
Both automorphisms and isomorphisms are types of transformations, but they differ in their specific properties. An automorphism preserves the structure of an object or system, while an isomorphism also preserves the operations and properties of the object or system.
Automorphisms are used in mathematics to study the symmetries and transformations of various objects and systems. They are also used to understand the structure and properties of mathematical structures, such as groups, rings, and fields.
Yes, automorphisms can be applied to real-world systems, such as physical objects, biological systems, and computer programs. They can be used to analyze and understand the structure and transformations of these systems.
Yes, there are many practical applications of automorphisms in fields such as physics, chemistry, biology, computer science, and engineering. For example, automorphisms are used in crystallography to study the symmetries of crystals, and in computer science to design and analyze algorithms and data structures.