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The spectral excess theorem for graphs with few eigenvalues whose distance-2 or distance-1-or-2 graph is strongly regular

Author
Dalfo, C.; Fiol, M.; Koolen, J.
Type of activity
Journal article
Journal
Linear and multilinear algebra
Date of publication
2018-07
DOI
https://doi.org/10.1080/03081087.2018.1491944 Open in new window
Project funding
Combinatorics of networks and computation
Repository
http://hdl.handle.net/2117/119639 Open in new window
URL
https://www.tandfonline.com/doi/abs/10.1080/03081087.2018.1491944 Open in new window
Abstract
We study regular graphs whose distance-2 graph or distance-1-or-2 graph is strongly regular. We provide a characterization of such graphs G (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex, where d+ 1 is the number of different eigenvalues of G. This can be seen as another version of the so-called spectral excess theorem, which characterizes in a similar way those regular graphs that are distance...
Citation
Dalfo, C., Fiol, M., Koolen, J. The spectral excess theorem for graphs with few eigenvalues whose distance-2 or distance-1-or-2 graph is strongly regular. "Linear and multilinear algebra", Juliol 2018.
Keywords
Distance-2 graph, Distance-regular graph, Predistance polynomials, Spectrum
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants