Periodica Mathematica Hungarica, vol.88, no.1, pp.59-67, 2024 (SCI-Expanded)
In this paper, we show that Frucht’s theorem holds in Borel setting. More specifically, we prove that any standard Borel group can be realized as the Borel automorphism group of a Borel graph. A slight modification of our construction also yields the following result in topological setting: Any Polish group can be realized as the homeomorphic automorphism group of a Σ20 -graph on a Polish space.