**Prerequisites**

Basic knowledge of graph theory, linear algebra (properties of real symmetric matrices) and algebra (in particular, permutation groups, group actions). Any bachelor level courses on graph theory, linear algebra, and group theory should be sufficient.

**Aim of the course**

In the first part of the course, we will cover symmetries of graph and eigenvalue techniques in graph theory. Topics will include vertex-transitivity, Cayley graphs, automorphism groups, eigenvalue interlacing and strongly regular graphs. In the second part of the course, we will study combinatorial designs, including (complete

imbalanced) block designs, symmetric designs, Hadamard Matrices, projective geometries, Latin squares and t-designs. We will study their constructions and point graphs, which will give some examples of strongly regular graphs, allowing us to applying techniques from the first half of the course.

**Lecturer**

Krystal Guo (UvA)

- Docent: Krystal Guo