**Speaker:** Jayakumar.R (PhD student, IMSc Chennai)

**Date:** 2nd April, 2019

**Time: **9:15pm-10:15pm

**Abstract:** In this talk, We will see the Cayley’s colour graphs and we will prove Frucht’s theorem which says “Given any finite group G there exists a connected simple graph X whose graph automorphism group is isomorphic to G”. Then if time permits I will try to give an idea of proof of the interesting problem “Given any finite group there exists a finite extension over rational numbers whose automorphism group is isomorphic to the given group” using the Frucht’s theorem to find such extensions.

**Prerequisite:** Basic Graph Theory.