In this paper, we introduce the language of a configuration and of t-point counts for distance-regular graphs (DRGs). Every t-point count can be written as a sum of $(t-1)$-point counts. This leads to a system of linear equations and inequalities for the t-point counts in terms of the intersection numbers, i.e., a linear constraint satisfaction problem (CSP). This language is a very useful tool for a better understanding of the combinatorial structure of distance-regular graphs. Among others we prove a new diameter bound for DRGs that is tight for the Biggs–Smith graph. We also obtain various old and new inequalities for the parameters of DRGs, including the diameter bounds by Terwilliger.

在本文中，我们介绍了距离正则图（DRG）的配置语言和t点计数。每个t点计数可以写为$（Ť-\mathrm{1个}）$点数。这就导致了一个线性方程组和关于t点计数的不等式的系统，这些系统以交点数表示，即线性约束满足问题（CSP）。该语言是一种非常有用的工具，可用于更好地理解距离正则图的组合结构。除其他外，我们证明了DRG的新直径范围对于Biggs-Smith图来说是紧密的。我们还获得了DRG参数的各种新旧不等式，包括Terwilliger的直径范围。