One of the central results in the representation theory of distance-regular graphs classifies distance-regular graphs with $\mu \ge 2$ and second largest eigenvalue ${\theta }_1=b_1-1$. In this paper we give a classification under the (weaker) approximate eigenvalue constraint ${\theta }_1\ge (1-\epsilon )b_1$ 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 of bounded diameter. This conjecture asserts that if X is a primitive distance-regular graph with n vertices, and X is not a Hamming graph or a Johnson graph, then the automorphism group $\mathrm{Aut}(X)$ has minimal degree $\ge cn$ for some constant $c>0$. It follows that $\mathrm{Aut}(X)$ satisfies strong structural constraints.

距离正则图表示理论的核心结果之一将距离正则图分类为 $\mu \ge 2$ 和第二大特征值 ${\theta }_1={乙}_1-1$. 在本文中，我们在（较弱的）近似特征值约束下给出了一个分类${\theta }_1\ge (1-\epsilon ){乙}_1$对于几何距离正则图类。作为一个应用，我们证实了八白关于有界直径距离正则图的自同构群的最小度的猜想。该猜想断言，如果X是具有n个顶点的原始距离正则图，并且X不是汉明图或约翰逊图，则自同构群$\mathrm{自动}(X)$ 学历最低 $\ge Cn$ 对于一些常数 $C>0$. 它遵循$\mathrm{自动}(X)$ 满足强结构约束。