Algebraic Combinatorics
An automorphism group is a mathematical structure that consists of all the automorphisms of a given object, typically a graph or algebraic structure, along with the operation of composition. It captures the idea of symmetry, showing how an object can be transformed into itself in different ways while preserving its overall structure. The study of automorphism groups helps in understanding the inherent symmetries and structural properties of graphs, revealing important relationships and patterns.
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