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Graphs and association schemes: higher-dimensional invariants and their applications

图和关联方案：高维不变量及其应用

基本信息

批准号：
22K03403
负责人：
Gavrilyuk Alexander
金额：
$ 2万
依托单位：
Shimane University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2022
资助国家：
日本
起止时间：
2022-04-01 至 2025-03-31
项目状态：
未结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22K03403/
关键词：
association scheme strongly regular graph graph isomorphism distance-regular graph

项目摘要

1. In collaboration with Ilia Ponomarenko (Saint-Petersburg department of the Steklov Institute of Mathematics) and Jin Guo (Hainan University), we determined the upper bound on the Weisfeiler-Leman dimension of permutation graphs. The paper is being prepared for submission.2. In collaboration with Sho Suda (National Defence Academy), we showed that a certain association scheme naturally arising from the Witt 11-design is uniquely determined by the structure constants of its Bose-Mesner algebra. The paper is under review.3. In collaboration with Vladislav Kabanov (Krasovskii Institute of Mathematics), we studied a prolific construction of strongly regular graphs that are decomposable into divisible design graphs and a Delsarte-Hoffman coclique. The paper is being prepared for submission.

1.与伊利亚Ponomarenko（圣彼得堡Steklov数学研究所）和Jin Guo（海南大学）合作，我们确定了置换图的Weisfeiler-Leman维数的上界。该文件正在准备提交。在与Sho苏达（国防科学院）的合作中，我们证明了从Witt 11-设计中自然产生的某种缔合方案是由其Bose-Mesner代数的结构常数唯一确定的。这份文件正在审查中。与Vladislav Kabanov（Krasovskii数学研究所）合作，我们研究了强正则图的多产构造，这些图可分解为可分设计图和Delsarte-Hoffman coclique。该文件正在编写中，以便提交。