| Project/Area Number |
16K05260
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Foundations of mathematics/Applied mathematics
|
|---|
| Research Institution | Shonan Institute of Technology |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
佐久間 雅 山形大学, 理学部, 准教授 (60323458)
|
|---|
| Project Period (FY) |
2016-04-01 – 2019-03-31
|
| Project Status |
Completed (Fiscal Year 2018)
|
| Budget Amount *help |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Keywords | グラフ理論 / グラフの自己同型 / グラフパズル / グラフの自己同型群 / グラフの石交換群 / コードダイアグラム / インターレースグラフ / Tutte多項式 / 離散数学 / 組合せ論 / 幾何グラフ |
|---|
| Outline of Final Research Achievements |
(1) Pebble exchange group of graphs: A whole set of graph automorphisms has a structure of a group, and it is called an automorphism group. We have studied what kind of graph automorphisms can be realized by repeatedly exchanging two pebbles(vertices) which are adjacent to each other on the graph.
(2) Expansion of chord diagrams: We have studied the chord expansion, which generates a pair of nonintersecting chords from a pair of intersecting chords. Beginning from a given chord diagram, by iterating the chord expansion, we have eventually a multiset of nonintersecting chord diagram. We have derived counting formulas for the multiset.
|
| Academic Significance and Societal Importance of the Research Achievements |
本研究課題では，グラフについての操作を研究対象としている．この操作が現実社会での行為と対応する場合には工学的な応用がある．例えば，ロボット工学において，複数ロボットの動作可能域としてのフィールドを盤グラフとし，複数ロボットの交換可能性を石グラフとするとき，フィールド上のロボットの動作は本研究課題におけるグラフパズルpuz(G,H)としてモデル化される．
|
