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On Completely Regular Clique Graphs

Research Project

Project/Area Number 26400022
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionInternational Christian University

Principal Investigator

Suzuki Hiroshi  国際基督教大学, 教養学部, 教授 (10135767)

Project Period (FY) 2014-04-01 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
KeywordsDistance-Regular Graph / DSRG / Association Scheme / Algebraic Graph Theory / Algebraic Combinatorics / 代数的組合せ論 / 距離正則グラフ / 代数的グラフ理論 / 有限幾何の普遍被覆 / アソシエーションスキーム / Terwilliger 代数 / グラフの表現論 / 有限幾何 / 距離正則クリークグラフ / CR Clique Graphs
Outline of Final Research Achievements

The original aim was to characterize classical distance-regular completely regular clique graphs satisfying the thin condition.
1. We clarified the structure of distance-regular completely regular clique graphs and established a way to determine whether the known distance-regular graphs with large diameter to have structures of completely regular clique graphs. It enabled us to determine completely regular clique graph structures, i.e., the choices of C, of all known families of distance-regular graphs with unbounded diameter.
2. We studied the universal C-cover of the associated distance-semiregular graphs and gave a finiteness condition of the universal C-cover when C is the collection of closed circuits of minimal length.

Academic Significance and Societal Importance of the Research Achievements

距離正則グラフ(DRG)のように、正則性の高いグラフにおいて、特定の、閉路の集合 C を持ち上げることのできる、C-普遍被覆を考えることが有効であること。特に、CRCG の構造を持っている場合には、付随する DSRG の、最短閉路の集合をC とし、その C-普遍被覆を考えることが本質的な意味を持つことを示し、DRG の研究に新しい視点を与えることができた。
DRG の中でも、Classical Parameter を持つものについては、ある意味で、それ自身が、普遍被覆となっていることから、C-単連結という性質で特徴づけ、分類へと向かい得る可能性を示すことができた。

Report

(5 results)
  • 2018 Final Research Report ( PDF )
  • 2017 Annual Research Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (9 results)

All 2017 2016 2014

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Open Access: 2 results) Presentation (6 results) (of which Invited: 2 results)

  • [Journal Article] Distance-Regular Graphs of Large Diameter That Are Completely Regular Clique Graphs2017

    • Author(s)
      Hiroshi Suzuki
    • Journal Title

      J. Algebraic Combin.

      Volume: - Issue: 3 Pages: 369-404

    • DOI

      10.1007/s10801-017-0808-9

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Completely Regular Clique Graphs, II2016

    • Author(s)
      Hiroshi Suzuki
    • Journal Title

      Journal of Algebraic Combinatorics

      Volume: 43 Issue: 2 Pages: 417-445

    • DOI

      10.1007/s10801-015-0639-5

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Completely Regular Clique Graphs2014

    • Author(s)
      Hiroshi Suzuki
    • Journal Title

      Journal of Algebraic Combinatorics

      Volume: 40

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] Lecture 1: Geometries of Distance-Regular Graphs, Lecture 2: Coverings and Homotopy of a Graph2017

    • Author(s)
      Hiroshi Suzuki
    • Organizer
      Mini Symposium on Algebraic Combinatorics
    • Place of Presentation
      De La Salle University, Philippines
    • Year and Date
      2017-03-14
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 距離正則グラフの幾何2017

    • Author(s)
      鈴木寛
    • Organizer
      小山工業高等専門学校数学談話会
    • Place of Presentation
      小山工業高等専門学校
    • Year and Date
      2017-01-27
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Coverings and Homotopy of a Graph2017

    • Author(s)
      鈴木寛
    • Organizer
      The 34th Algebraic Combinatorics Symposium
    • Related Report
      2017 Annual Research Report
  • [Presentation] t-Designs Over a Finite Field2016

    • Author(s)
      Hiroshi Suzuki
    • Organizer
      International Workshop on Algebraic Combinatorics
    • Place of Presentation
      Anhui University, China
    • Year and Date
      2016-10-31
    • Related Report
      2016 Research-status Report
  • [Presentation] Completely regular clique graphs with thick lines2016

    • Author(s)
      鈴木寛
    • Organizer
      第28回有限群論草津セミナー
    • Place of Presentation
      草津セミナーハウス
    • Year and Date
      2016-07-29
    • Related Report
      2016 Research-status Report
  • [Presentation] Completely Regular Clique Graphs2016

    • Author(s)
      鈴木寛
    • Organizer
      第 33 回代数的組合せ論シンポジウム
    • Place of Presentation
      ピアザ;淡海 (大津市)
    • Year and Date
      2016-06-23
    • Related Report
      2016 Research-status Report

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Published: 2014-04-04   Modified: 2020-03-30  

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