A quantum Frucht's theorem and quantum automorphisms of quantum Cayley graphs

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Quantum automorphism group arises from finite quantum group using quantum graphs, suggesting new symmetry insights.

Quantum graph uniquely represents the structure of finite quantum groups, enhancing symmetry understanding.
Significant findings showed that each finite quantum group can be modeled by a quantum automorphism group.
Construction involves quantum Cayley graphs systematically combined to yield undirected finite quantum graphs.
Implications point to exploring the properties of non‐abelian finite groups and their quantum rigidity.

Brannan et al. (2025) studied this question.

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