On a Koolen -- Park inequality and Terwilliger graphs

The Terwilliger algebra of the twisted Grassmann graph: the thin case

The Terwilliger algebra $T(x)$ of a finite connected simple graph $Γ$ with respect to a vertex $x$ is the complex semisimple matrix algebra generated by the adjacency matrix $A$ of $Γ$ and the diagonal matrices $E_i^*(x)=\operatorname{diag}(v_i)$ $(i=0,1,2,\dots)$, where $v_i$ denotes the characteristic vector of the set of vertices at distance $i$ from $x$. The twisted Grassmann graph $\tilde{J}_q(2D+1,D)$ discovered by Van Dam and Koolen in 2005 has two orbits of the automorphism group on its vertex set, and it is known that one of the orbits has the property that $T(x)$ is thin whenever $x$…

丰富正则图的Ricci曲率、直径与特征值

Ricci curvature, diameter and eigenvalues of amply regular graphs

本文利用改进的Lin--Lu--Yau曲率估计和新的Bakry--Émery曲率估计，证明了丰富正则图直径上界猜想的一个较弱版本，推进了Terwilliger有限性猜想，并应用于特征值、等周常数和扩张性质。