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arXiv · 2611.02986

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 $(d,b,α,β)=(d,2,1,2^d-2)$ 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.

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Alexander L. Gavrilyuk, Janoš Vidali. 2026-11-02. On local spectra of classical distance-regular graphs with $b = 2$. https://arxiv.org/abs/2611.02986

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