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The Laplacian spectral excess theorem for distance-regular graphs

Autor
Van Dam, E.; Fiol, M.
Tipus d'activitat
Article en revista
Revista
Linear algebra and its applications
Data de publicació
2014-10-01
Volum
458
Pàgina inicial
245
Pàgina final
250
DOI
https://doi.org/10.1016/j.laa.2014.06.001 Obrir en finestra nova
Projecte finançador
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 Obrir en finestra nova
Resum
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.
Paraules clau
Distance-regular graph, Laplacian spectrum, NONREGULAR GRAPHS, Orthogonal polynomials, POLYNOMIALS, Spectral excess theorem
Grup de recerca
COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions

Participants