The influence of Miroslav Fiedler on spectral graph theory

This note is a write up of a talk given at the ILAS meeting in Braunschweig, 2011, at the minisymposium celebrating the 80th birthday of Miroslav Fiedler. The purpose of the talk is to outline the impact of Fiedler’s work on the development of spectral graph theory. Fiedler is best known for putting forward the algebraic connectivity and its eigenvector. These two topics were genuine gold strikes which have motivated thousands of studies in pure and applied science. But there is more in Fiedler’s work that influences spectral graph theory, and still more waiting to be discovered.