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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

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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.
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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
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Linear & Multilinear Algebra, 2019, vol. 67, num. 12, p. 2373-2381
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  • Articles publicats (Matemàtica) [263]

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