• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

A study of deformation operations of graphs

Research Project

Project/Area Number 16K05260
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Foundations of mathematics/Applied mathematics
Research InstitutionShonan Institute of Technology

Principal Investigator

Nakamigawa Tomoki  湘南工科大学, 工学部, 教授 (20386890)

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.

Report

(4 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (13 results)

All 2018 2017 2016 Other

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results) Presentation (7 results) (of which Int'l Joint Research: 4 results) Remarks (3 results)

  • [Journal Article] The Expansion of a Chord Diagram and the Tutte Polynomial2018

    • Author(s)
      Tomoki Nakamigawa and Tadashi Sakuma
    • Journal Title

      Discrete Mathematics

      Volume: 341 Issue: 6 Pages: 1573-1581

    • DOI

      10.1016/j.disc.2018.02.015

    • Related Report
      2018 Annual Research Report 2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] The Expansion of a Chord Diagram and the Tutte Polynomial(extended abstract)2017

    • Author(s)
      T. Nakamigawa and T. Sakuma
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 61 Pages: 917-923

    • DOI

      10.1016/j.endm.2017.07.054

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Enumeration Problems on the Expansion of a Chord Diagram2016

    • Author(s)
      T. Nakamigawa
    • Journal Title

      Electronic Notes in Discrete Mathematics

      Volume: 54 Pages: 51-56

    • DOI

      10.1016/j.endm.2016.09.010

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Pebble Exchange on Graphs and Graph Automorphism2018

    • Author(s)
      Tomoki Nakamigawa
    • Organizer
      10th International Colloquium on Graph Theory and combinatorics, July 9-13, 2018 at University Claude Bernard Lyon
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Pebble Exchange Group of Graphs2018

    • Author(s)
      Tadashi Sakuma
    • Organizer
      6th Asian Conference on Nonlinear Analysis and Optimization, November 5-9, 2018 at Okinawa Japan
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 一般三角形分割の出次数列について2018

    • Author(s)
      中上川 友樹
    • Organizer
      応用数学合同研究集会,龍谷大学,2018年12月.
    • Related Report
      2018 Annual Research Report
  • [Presentation] The expansion of a chord diagram and the Tutte polynomial2017

    • Author(s)
      T. Nakamigawa and T. Sakuma
    • Organizer
      The European Conference on Combinatorics, Graph Theory and Applications (EUROCOMB'17)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] グラフの石交換群2017

    • Author(s)
      中上川友樹,加藤立隆,佐久間雅
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] コードダイアグラムの展開とTutte多項式2016

    • Author(s)
      中上川 友樹,佐久間 雅
    • Organizer
      2016年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県大津市)
    • Year and Date
      2016-12-15
    • Related Report
      2016 Research-status Report
  • [Presentation] Enumeration Problems on the Expansion of a Chord Diagram2016

    • Author(s)
      T. Nakamigawa
    • Organizer
      Discrete Mathematics Days - JMDA16
    • Place of Presentation
      カタルーニャ工科大学(スペイン,バルセロナ)
    • Year and Date
      2016-07-05
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Remarks] 湘南工科大学 情報工学科 教員紹介 中上川友樹

    • URL

      http://www.shonan-it.ac.jp/teachers/information/t-nakamigawa/

    • Related Report
      2018 Annual Research Report
  • [Remarks] 湘南工科大学ホームページの教員情報

    • URL

      http://www.shonan-it.ac.jp/teachers/information/t-nakamigawa/

    • Related Report
      2017 Research-status Report
  • [Remarks] 湘南工科大学教員情報

    • URL

      http://www.shonan-it.ac.jp/contents/teachers/information/t-nakamigawa/index.html

    • Related Report
      2016 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2020-03-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi