Graphs and association schemes: higher-dimensional invariants and their applications
| Project/Area Number |
22K03403
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12030:Basic mathematics-related
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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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| Project Status |
Discontinued (Fiscal Year 2023)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2024: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2023: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2022: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | association scheme / strongly regular graph / graph isomorphism / distance-regular graph |
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| Outline of Research at the Start |
We will continue investigation of 3-tuple intersection numbers of association schemes, in particular, the Grassmann schemes. We plan to study how some graph operations affect the WL-dimension. The main research target will be a proof that the ISO problem of circular-arc graphs is polynomial time.
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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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Report
(2 results)
Research Products
(15 results)
