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 |
Section | 一般 |
Review Section |
Basic Section 12030:Basic mathematics-related
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Research Institution | Shimane University |
Principal Investigator |
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Project Period (FY) |
2022-04-01 – 2025-03-31
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Project Status |
Granted (Fiscal Year 2022)
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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 |
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. 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.
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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. Writing the proof of the upper bound on the Weisfeiler-Leman dimension of permutation graphs took slightly longer than expected (due to only the remote communication with co-authors and the overall difficulty of the proof). On the other hand, the joint work with Sho Suda was completed very quickly during his research stay at Shimane University.
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Strategy for Future Research Activity |
1. We plan to significantly improve the Weisfeiler-Leman dimension of permutation graphs by using some new approach (joint with Ponomarenko). 2. Using the above result, we plan to determine the Weisfeiler-Leman dimension of circular-arc graphs without 3-coclique (joint with Ponomarenko, Nedela, Zeman). 3. We will study 3-designs in Hamming association schemes. In particular, we will obtain some classification results by using triple intersection numbers. 4. We plan to investigate the Weisfeiler-Leman dimension of graphs related to semifield projective planes.
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Report
(1 results)
Research Products
(8 results)