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The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues

Author
Fiol, M.
Type of activity
Journal article
Journal
Journal of algebraic combinatorics
Date of publication
2016-06-01
Volume
43
Number
4
First page
827
Last page
836
DOI
https://doi.org/10.1007/s10801-015-0654-6 Open in new window
Project funding
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
Optimization techniques in graph theory, groups, and combinatorics. Applications to networks, algorithms, and communication protocols
Repository
http://hdl.handle.net/2117/100474 Open in new window
URL
http://link.springer.com/article/10.1007%2Fs10801-015-0654-6 Open in new window
Abstract
Let Gamma be a distance-regular graph with diameter d and Kneser graph K = Gamma(d), the distance-d graph of Gamma. We say that Gamma is partially antipodal when K has fewer distinct eigenvalues than Gamma. In particular, this is the case of antipodal distance-regular graphs (K with only two distinct eigenvalues) and the so-called half-antipodal distance-regular graphs (K with only one negative eigenvalue). We provide a characterization of partially antipodal distance-regular graphs (among regul...
Citation
Fiol, M. The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues. "Journal of algebraic combinatorics", 1 Juny 2016, vol. 43, núm. 4, p. 827-836.
Keywords
Distance-regular graph, Kneser graph, Partial antipodality, Polynomials, Predistance polynomials, Spectrum
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

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