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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
Electronic notes in discrete mathematics
Date of publication
2015-01-01
Volume
49
First page
457
Last page
463
DOI
https://doi.org/10.1016/j.endm.2015.06.064 Open in new window
Repository
http://hdl.handle.net/2117/85047 Open in new window
Abstract
Let G be a distance-regular graph with diameter d and Kneser graph K=Gd, the distance-d graph of G. We say that G is partially antipodal when K has fewer distinct eigenvalues than G. 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 distin...
Citation
Fiol, M. The spectral excess theorem for distance-regular graphs having distance-d graph with fewer distinct eigenvalues. "Electronic notes in discrete mathematics", 01 Gener 2015, vol. 49, p. 457-463.
Keywords
Distance-regular graph, Kneser graph, Partial antipodality, Predistance polynomials, Spectrum
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

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