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  • Kivva, Bohdan

    arXiv.org, 12/2019
    Paper, Journal Article

    One of the central results in the representation theory of distance-regular graphs classifies distance-regular graphs with \(\mu\geq 2\) and second largest eigenvalue \(\theta_1= b_1-1\). In this paper we give a classification under the (weaker) approximate eigenvalue constraint \(\theta_1\geq (1-\varepsilon)b_1\) 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.