A unified view of inequalities for distance-regular graphs

In this talk, 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.

This is joint work with prof Arnold Neumaier. The results are published in Journal of Combinatorial Theory, Series B, and the paper is available at https://doi.org/10.1016/j.jctb.2020.09.015

Everyone is welcome and encouraged to attend.

Hope to see you there!