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On local spectra of classical distance-regular graphs with $b = 2$ — arXiv:2611.02986

Source: arXiv (en)
Original: https://arxiv.org/abs/2611.02986
License (as archived): CC0-1.0
Archived: 2026-11-03T18:50:40.155Z
SHA-256 of the archived text: 639d129fa8363c98ed814537c7609c4b0e0866a0fa68a0e8b168fe69b44972b9
Stable URL of this page: https://metraipolis.com/documento/dc_eb86aba60577

How to cite

On local spectra of classical distance-regular graphs with $b = 2$ — arXiv:2611.02986 — arXiv (en), https://arxiv.org/abs/2611.02986 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_eb86aba60577 (Metraipolis archive dc_eb86aba60577, sha256 639d129fa8363c98ed814537c7609c4b0e0866a0fa68a0e8b168fe69b44972b9)

BibTeX

@misc{dceb86aba60577,
  title = {On local spectra of classical distance-regular graphs with $b = 2$ — arXiv:2611.02986},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2611.02986},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_eb86aba60577; sha256 639d129fa8363c98ed814537c7609c4b0e0866a0fa68a0e8b168fe69b44972b9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2611.02986. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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 $(d,b,\alpha,\beta)=(d,2,1,2^d-2)$ passed all known feasibility conditions and required a deeper combinatorial analysis, from which nonexistence has been derived whenever $d \ge 9$. 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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.CO, nuovi lavori del giorno).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2611.02986 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-11-03T18:15:38.100Z dalla pagina https://arxiv.org/list/math.CO/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).