There are only finitely many distance-regular graphs of fixed valency greater than two

DOI10.1016/j.aim.2014.09.025zbMath1303.05044arXiv0909.5253OpenAlexW2080815958WikidataQ56673208 ScholiaQ56673208MaRDI QIDQ475256

Sejeong Bang, Jack H. Koolen, Arturas Dubickas, Vincent L. Moulton

Publication date: 26 November 2014

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.5253

zbMATH Keywords

distance-regular graphsBannai-Ito conjectureChristoffel numbersothogonal polynomialssims conjecture

Mathematics Subject Classification ID

Distance in graphs (05C12)

Related Items (21)

The search for small association schemes with noncyclotomic eigenvalues ⋮ On bounding the diameter of a distance-regular graph ⋮ Classification of partially metric Q-polynomial association schemes with \(m_1=4\) ⋮ On distance-regular graphs with smallest eigenvalue at least \(- m\) ⋮ Spectral determinations and eccentricity matrix of graphs ⋮ Nonexistence of exceptional imprimitive \(Q\)-polynomial association schemes with six classes ⋮ Classifying the globally rigid edge‐transitive graphs and distance‐regular graphs in the plane ⋮ An inequality involving the second largest and smallest eigenvalue of a distance-regular graph ⋮ Geometric aspects of 2-walk-regular graphs ⋮ On geometric distance-regular graphs with diameter three ⋮ A new characterization of the dual polar graphs ⋮ On the Calculation of Multiplicities forP-PolynomialC-Algebras ⋮ Which graphs have non-integral spectra? ⋮ Non-bipartite distance-regular graphs with a small smallest eigenvalue ⋮ On the spectral gap and the automorphism group of distance-regular graphs ⋮ Recent progress on graphs with fixed smallest adjacency eigenvalue: a survey ⋮ Distance-regular Cayley graphs with small valency ⋮ Distance-regular graphs without 4-claws ⋮ Scaling limits for the Gibbs states on distance-regular graphs with classical parameters ⋮ A survey of semisimple algebras in algebraic combinatorics ⋮ Non-bipartite distance-regular graphs with diameters 5, 6 and a smallest eigenvalue

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