The Laplacian spectral excess theorem for distance-regular graphs
Combinatorics
2014-07-28 v2
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 note we prove the corresponding result by using the Laplacian spectrum without requiring regularity of G.
Cite
@article{arxiv.1405.0169,
title = {The Laplacian spectral excess theorem for distance-regular graphs},
author = {Edwin R. van Dam and Miquel Angel Fiol},
journal= {arXiv preprint arXiv:1405.0169},
year = {2014}
}