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On local spectra of classical distance-regular graphs with b = 2

  • Alexander L. Gavrilyuk
  • Janoš Vidali
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Abstract

Using a combination of spectral techniques and combinatorial counts, we prove a number of non-existence results for putative distance-regular graphs with classical parameters, focusing on the case b=2. Among those, the case (d,b,α,β)=(d,2,1,2d−2) passed all known feasibility conditions and required a deeper combinatorial analysis, from which nonexistence has been derived whenever d ≥ 9. In doing so, we constructed a new family of regular graphs with four distinct eigenvalues which would have been local graphs in such a distance-regular graph.

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Cite

BibTeXRIS
BibTeX
@misc{gavrilyuk2026local,
  title = {{On local spectra of classical distance-regular graphs with $b = 2$}},
  author = {Alexander L. Gavrilyuk and Janoš Vidali},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.02986},
  eprint = {2611.02986},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.02986},
}
RIS
TY  - UNPB
TI  - On local spectra of classical distance-regular graphs with b = 2
AU  - Alexander L. Gavrilyuk
AU  - Janoš Vidali
PY  - 2026
DA  - 2026/11/02
PB  - arXiv
DO  - 10.48550/arxiv.2611.02986
UR  - https://arxiv.org/abs/2611.02986
AB  - Using a combination of spectral techniques and combinatorial counts, we prove a number of non-existence results for putative distance-regular graphs with classical parameters, focusing on the case b=2. Among those, the case (d,b,α,β)=(d,2,1,2^d−2) passed all known feasibility conditions and required a deeper combinatorial analysis, from which nonexistence has been derived whenever d ≥ 9. In doing so, we constructed a new family of regular graphs with four distinct eigenvalues which would have been local graphs in such a distance-regular graph.
ER  -