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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2018-07-13Suggested 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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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.
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Linear & Multilinear Algebra, 2019, vol. 67, num. 12, p. 2373-2381European research projects
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