2026-04-18T01:25:53Zhttps://recercat.cat/oai/requestoai:recercat.cat:10459.1/675112025-03-16T19:56:14Zcom_2072_3622col_2072_479130
RECERCAT
author
Dalfó, Cristina
author
Fiol Mora, Miguel Ángel
author
Koolen, Jack
2019-11-11T11:45:09Z2019-11-11T11:45:09Z2018-07-132019-11-11T11:45:09Z
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.Research of C. Dalfó and M. A. Fiol is partially supported by Agència de Gestió d'Ajuts Universitaris i de Recerca (AGAUR) under project 2017SGR1087. Research of J. Koolen is partially supported by the National Natural Science Foundation of China under project No. 11471009, and the Chinese Academy of Sciences under its ‘100 talent’ programme. The research of C. Dalfó has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 734922.
(c) Taylor & Francis, 2019 info:eu-repo/semantics/openAccess
Distance-regular graph
Distance-2 graph
Spectrum
Predistance polynomials
The spectral excess theorem for graphs with few eigenvalues whose distance- 2 or distance-1-or-2 graph is strongly regular
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion