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arXiv · 1912.11427

A characterization of Johnson and Hamming graphs and proof of Babai's conjecture

Bohdan Kivva
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Abstract

One of the central results in the representation theory of distance-regular graphs classifies distance-regular graphs with $μ\geq 2$ and second largest eigenvalue $θ_1= b_1-1$. In this paper we give a classification under the (weaker) approximate eigenvalue constraint $θ_1\geq (1-\varepsilon)b_1$ for the class of geometric distance-regular graphs. As an application, we confirm Babai's conjecture on the minimal degree of the automorphism group of distance-regular graphs.

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Bohdan Kivva. 2019-12-24. A characterization of Johnson and Hamming graphs and proof of Babai's conjecture. https://doi.org/10.1016/j.jctb.2021.07.003

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