The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues
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hdl:2117/100474
Tipus de documentArticle
Data publicació2016-06-01
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Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
ProjecteOPTIMIZACION Y PROBLEMAS EXTREMALES EN TEORIA DE GRAFOS Y COMBINATORIA. APLICACIONES A LAS REDES DE COMUNICACION. (MICINN-MTM2011-28800-C02-01)
TECNICAS DE OPTIMIZACION EN TEORIA DE GRAFOS, GRUPOS Y COMBINATORIA. APLICACIONES A REDES, ALGORITMOS Y PROTOCOLOS DE COMUNICACION. (MINECO-MTM2014-60127-P)
TECNICAS DE OPTIMIZACION EN TEORIA DE GRAFOS, GRUPOS Y COMBINATORIA. APLICACIONES A REDES, ALGORITMOS Y PROTOCOLOS DE COMUNICACION. (MINECO-MTM2014-60127-P)
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 regular graphs with d + 1 distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex. This can be seen as a more general version of the so-called spectral excess theorem, which allows us to characterize those distance-regular graphs which are half-antipodal, antipodal, bipartite, or with Kneser graph being strongly regular.
Descripció
The final publication is available at Springer via http://dx.doi.org/10.1007/s10801-015-0654-6
CitacióFiol, 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.
ISSN0925-9899
Versió de l'editorhttp://link.springer.com/article/10.1007%2Fs10801-015-0654-6
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