Graph theory seminar - Miquel Angel Fiol Mora

The Laplacian Spectral Excess Theorem for Distance-regular Graphs

Abstract: 

The spectral excess theorem states that, in a regular graph $G$, the average excess, which is the mean of the numbers of vertices at maximum distance from a vertex, is bounded above by the spectral excess (a number that is computed by using the adjacency spectrum of $G$), and $G$ is distance-regular if and only if equality holds. In this talk we prove the corresponding result by using the Laplacian spectrum without requiring regularity of $G$. (Joint work with E.R. van Dam.)