2023 Fiscal Year Research-status Report
Graphs and association schemes: higher-dimensional invariants and their applications
| Project/Area Number |
22K03403
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| Research Institution | Shimane University |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2025-03-31
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| Keywords | association scheme / strongly regular graph / graph isomorphism |
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| Outline of Annual Research Achievements |
1. With Ponomarenko (Saint-Petersburg, the Steklov Institute of Mathematics) and Guo, Cai (Hainan University), we constructed exponentially many strongly regular graphs with bounded Weisfeiler-Leman dimension. The paper is under review.
2. With Suda (National Defence Academy), we showed that The paper is prepared for submission.
3. With Kabanov (Krasovskii Institute of Mathematics), we determined all strongly regular graphs that are decomposable into divisible design graphs and a Delsarte clique. The paper is prepared for submission.
4. With Abiad, Khramova (Eindhoven University), we computed a linear programmig bound for sum-rank-metric codes. The paper is prepared for submission.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
We expected to obtain the above results.
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| Strategy for Future Research Activity |
1. We plan to improve the Weisfeiler-Leman dimension of permutation graphs
and use this to to determine the Weisfeiler-Leman dimension of circular-arc
graphs without 3-coclique (joint with Ponomarenko, Nedela, Zeman).
2. We plan to study coherent configurations of Cartesian products of graphs.
This may help to improve linear programming bounds for sum-rank-metirc codes.
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