The study of spectral graph determination is a central and fascinating topic in spectral graph theory and algebraic combinatorics. This area investigates the spectral characterization of various classes of graphs, develops methods for constructing and distinguishing cospectral nonisomorphic graphs, and analyzes the conditions under which the spectrum of a graph uniquely determines its structure. In the first part of the seminar, we present both classical results and recent advances in spectral graph determination.
The study of graph symmetries and different notions of transitivity is also of fundamental interest in algebraic graph theory. In the second part of the talk, we examine transitivity properties of Gilbert graphs and their complements, and discuss the main ideas underlying these results.