2026-04-18T00:12:13Zhttps://recercat.cat/oai/request

oai:recercat.cat:10459.1/675112025-03-16T19:56:14Zcom_2072_3622col_2072_479130

00925njm 22002777a 4500 dc Dalfó, Cristina author Fiol Mora, Miguel Ángel author Koolen, Jack author 2019-11-11T11:45:09Z 2019-11-11T11:45:09Z 2018-07-13 2019-11-11T11:45:09Z 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. 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