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

• 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

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Ilia Ponomarenko（斯捷克洛夫数学研究所圣彼得堡系）和郭金（海南大学）合作，确定了排列图Weisfeiler-Leman维数的上限。论文正在准备提交中。2．我们与 Sho Suda（国防学院）合作，证明了 Witt 11 设计自然产生的某种关联方案是由其 Bose-Mesner 代数的结构常数唯一确定的。论文正在审稿中。3．我们与 Vladislav Kabanov（克拉索夫斯基数学研究所）合作，研究了强正则图的丰富构造，这些图可分解为可整除的设计图和 Delsarte-Hoffman 群。该论文正在准备提交。

项目成果

m-ovoids of elliptic polar space

椭圆极空间的m-卵形

• 发表时间: 2023
• 作者: Alexander Gavrilyuk;Alexander Gavrilyuk;Alexander Gavrilyuk
• 通讯作者: Alexander Gavrilyuk

University of Science and Technology/Hainan University(中国)

科学技术大学/海南大学（中国）

Steklov Mathematics Institute/Krasovskii Institute of Mathematics(ロシア連邦)

斯特克洛夫数学研究所/克拉索夫斯基数学研究所（俄罗斯联邦）

An algebraic approach to the isomorphism problem of some graph classes

一些图类同构问题的代数方法

• 发表时间: 2023
• 作者: Alexander Gavrilyuk

Strongly regular decomposable into a divisible design graph and a coclique

强正则可分解为可分的设计图和小团

• 发表时间: 2023
• 作者: Alexander Gavrilyuk;Alexander Gavrilyuk
• 通讯作者: Alexander Gavrilyuk