高度正则图的结构理论与应用

Distance-(bi)regular graphs, which have nice algebraic property and combinatorial structures, not only play important roles in algebraic combinatorics, but also have many important applications in many areas such as extremal combinatorics, designs and hypergraphs. This project contains the following research: the Terwilliger algebra of distance-biregular graphs; spectrum of distance-regular graphs; the substructures of distance-regular graphs and their applications in extremal combinatorics, pooling designs and mixed hypergraphs.

距离（双）正则图具有很好的代数性质和组合结构, 它们的研究不仅在代数组合学中有重要的意义, 而且在极值组合学,设计,超图等中有重要的应用．本项目拟研究距离双正则图的Terwilliger代数；距离正则图的谱；距离正则图的子结构,及其在极值组合学,池设计和超图等中的应用．

距离正则图具有很好的代数性质和组合结构, 它们的研究不仅在代数组合学中有重要的意义, 而且在极值组合学、设计、超图等中有重要的应用．本项目在结合方案、距离正则图、 Terwilliger代数、度量维数、识别码、极值组合学、池设计、超图、典型群的几何学、群与图等，取得一些列重要研究成果，一共发表45篇SCI学术论文。