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math.CO2026

Asymptotic stability of Cayley graphs on abelian groups

Binzhou Xia, Zhishuo Zhang, Shasha Zheng

For a finite group , we say that a Cayley graph on is a most rigid representation (MRR) of if its full automorphism group has the smallest possible order among all C…

math.CO2022

Asymptotic enumeration of graphical regular representations

Binzhou Xia, Shasha Zheng

We estimate the number of graphical regular representations (GRRs) of a given group with large enough order. As a consequence, we show that almost all finite Cayley graphs have ful…