Spectral graph theory

Objectives and outcomes

Introducing student to the theoretical and practical aspects of the spectral graph theory. Upon completion of the course, students have the knowledge about the spectral graph theory and are familiar with some of its applications. They are trained for independent research work in that field.


Matrix representation of graphs and their spectra. Basic features of graph spectrum. Operations on graphs and the resulting spectra. Relations between the spectral and structural properties of graphs. Divisors of graphs. Characterisation of graphs via their spectra. The spectral techniques in graph theory and combinatorics. Open problems of spectral graph theory. Applications in computer science, chemistry and physics. Software packages and their implementation.

Research work

Students broaden their knowledge acquired in lectures by reading scientific magazines and other literature.