A unified view of inequalities for distance-regular graphs, part I
A unified view of inequalities for distance-regular graphs, part I
复制标题
DOI：
10.1016/j.jctb.2020.09.015
复制
发表时间：
2020-10
期刊：
影响因子：
--
通讯作者：
A. Neumaier;Safet Penjić
中科院分区：
文献类型：
--
作者：
A. Neumaier;Safet Penjić
本文介绍了距离正则图的一种构型语言和t点计数语言。每个t点计数可以写成(t−1)点计数的和。这就产生了一个关于t点计数的线性方程组和关于交点数的不等式，即线性约束满足问题(CSP)。这种语言对于更好地理解距离正则图的组合结构是非常有用的工具。其中，我们证明了DRG的一个新的直径界，它对Biggs-Smith图是紧的。我们还得到了关于DRGs参数的各种旧的和新的不等式，包括Terweiliger的直径界限。
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, ie, 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.