Algebraic Graph Theory

Main part of the course is the study of symmetries of graphs, and in particular graph families having high degree of symmetry such as vertex-transitive graphs, edge-transitive graphs, arc-transitive graphs and Cayley graphs. The method for counting the number of non-isomorphic graphs with a given number of vertices will be explained. Four standard graph products (Cartesian, direct, strong and lexicographic) will be introduced and their symmetries will be studied. Several open problems will be discussed, like for example the problem of existence of hamilton cycles in vertex-transitive graphs.
Distance-regular graphs and strongly-regular graphs will be studied.
The computer package MAGMA will be introduced and used for basic computations related to the symmetries of graphs.
Prerequisits: Students are expected to have basic group theory knowledge as well as basic knowledge from permutation group theory.