Loading...
Loading...

Go to the content (press return)

The Laplacian spectral excess theorem for distance-regular graphs

Author
Van Dam, E.; Fiol, M.
Type of activity
Journal article
Journal
Linear algebra and its applications
Date of publication
2014-10-01
Volume
458
First page
245
Last page
250
DOI
https://doi.org/10.1016/j.laa.2014.06.001 Open in new window
Project funding
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
URL
http://www.sciencedirect.com/science/article/pii/S0024379514003656 Open in new window
Abstract
The spectral excess theorem states that, in a regular graph Gamma, 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 Gamma), and Gamma 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 Gamma. (C) 2014 Elsevier Inc. All rights reserved.
Keywords
Distance-regular graph, Laplacian spectrum, NONREGULAR GRAPHS, Orthogonal polynomials, POLYNOMIALS, Spectral excess theorem
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants