| 研究課題/領域番号 |
22K03403
|
|---|
| 研究種目 |
基盤研究(C)
|
| 配分区分 | 基金 |
|---|
| 応募区分 | 一般 |
|---|
| 審査区分 |
小区分12030:数学基礎関連
|
|---|
| 研究機関 | 島根大学 |
|---|
研究代表者 |
|
|---|
| 研究期間 (年度) |
2022-04-01 – 2025-03-31
|
| 研究課題ステータス |
交付 (2022年度)
|
| 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)
|
|---|
| キーワード | association scheme / strongly regular graph / graph isomorphism / distance-regular graph |
|---|
| 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.
|
| 研究実績の概要 |
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.
|
| 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. 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.
|
| 今後の研究の推進方策 |
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.
|
