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

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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.