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

Dalfó, Cristina; Fiol, Miguel Angel; Koolen, Jack

doi:https://doi.org/10.1080/03081087.2018.1491944

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Issue date

2018-07-13

Author

Dalfó, Cristina

Fiol, Miguel Angel

Koolen, Jack

Suggested citation

Dalfó, Cristina; Fiol, Miguel Angel; Koolen, Jack; . (2018) . The spectral excess theorem for graphs with few eigenvalues whose distance- 2 or distance-1-or-2 graph is strongly regular. Linear & Multilinear Algebra, 2019, vol. 67, num. 12, p. 2373-2381. https://doi.org/10.1080/03081087.2018.1491944.

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 Γ (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 Γ. 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-regular.

URI

http://hdl.handle.net/10459.1/67511

DOI

https://doi.org/10.1080/03081087.2018.1491944

Is part of

Linear & Multilinear Algebra, 2019, vol. 67, num. 12, p. 2373-2381