| 研究課題/領域番号 |
22K03403
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| 研究種目 |
基盤研究(C)
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| 配分区分 | 基金 |
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| 応募区分 | 一般 |
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| 審査区分 |
小区分12030:数学基礎関連
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| 研究機関 | 島根大学 |
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研究代表者 |
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| 研究期間 (年度) |
2022-04-01 – 2025-03-31
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| 研究課題ステータス |
中途終了 (2023年度)
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| 配分額 *注記 |
3,120千円 (直接経費: 2,400千円、間接経費: 720千円)
2024年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2023年度: 910千円 (直接経費: 700千円、間接経費: 210千円)
2022年度: 1,300千円 (直接経費: 1,000千円、間接経費: 300千円)
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| キーワード | association scheme / strongly regular graph / graph isomorphism / distance-regular graph |
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| 研究開始時の研究の概要 |
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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| 研究実績の概要 |
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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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
We expected to obtain the above results.
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| 今後の研究の推進方策 |
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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