Structure of subgraphs in a distance-regular graph

2008 Fiscal Year Final Research Report

• Project/Area Number: 17540114
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka Kyoiku University
• Principal Investigator: HIRAKI Akira Osaka Kyoiku University, 教育学部, 准教授 (90294181)
• Project Period (FY): 2005 – 2008
• Keywords: 代数的組合せ論 / 距離正則グラフ

Research Abstract

「任意の2点に対して、その2点を含み2点間の距離を直径とするような強閉(Strongly closed)な部分グラフが存在する」という性質を持つ距離正則グラフを研究した。その具体例としては「Odd, Doubled Odd, Doubled Grassmann, Hamming, Dual polar, Hermitian forms」という距離正則グラフの無限系列に属するグラフがよく知られている。本研究においては、いくつかの条件の下で、そのような距離正則グラフは上記の無限系列に属するグラフのいずれかであることを証明した。

Research Products

• [Journal Article] A Characterization of the Hamming graphs by strongly closed subgraphs (2008)
  • Author(s): A. HIRAKI
  • Journal Title: European Journal of Combinatorics, 29 no. 1 Pages: 1603-1616
  • Peer Reviewed
• [Journal Article] Strongly closed subgraphs in a distance-regular graph with c_2 > 1 (2008)
  • Author(s): A. HIRAKI
  • Journal Title: Graphs and Combinatorics 24 no. 6 Pages: 537-550
  • Peer Reviewed
• [Journal Article] A Characterization of the Odd graphs and doubled Odd graphs with a few of thier intersection numbers (2007)
  • Author(s): A. HIRAKI
  • Journal Title: European Journal of Combinatorics, 28 no. 1 Pages: 246-257
  • Peer Reviewed
• [Journal Article] Delsarte clique graphs (2007)
  • Author(s): S. BANG, A. HIRAKI, J. KOOLEN
  • Journal Title: European Journal of Combinatorics, 28 no. 2 Pages: 501-516
  • Peer Reviewed
• [Journal Article] Improving diameter bounds for distance-regular graphs (2006)
  • Author(s): S. BANG, A. HIRAKI, J. KOOLEN
  • Journal Title: European Journal of Combinatorics, 27 no. 1 Pages: 79-89
  • Peer Reviewed
• [Journal Article] Application of the retracing method for distance-regular graphs (2005)
  • Author(s): A. HIRAKI
  • Journal Title: European Journal of Combinatorics 26 no. 5 Pages: 717-727
  • Peer Reviewed
• [Journal Article] A generalization of an inequality of Brouwer-Wilbrink (2005)
  • Author(s): A. HIRAKI, J. KOOLEN
  • Journal Title: Journal of Combinatorial Theory Ser. A 109 no. 1 Pages: 181-188
  • Peer Reviewed
• [Presentation] 6th Korea-Japan Workshop on Algebra and Combinatorics (2009)
  • Author(s): A. HIRAKI
  • Place of Presentation: 釜山国立大学
  • Year and Date: 2009-02-10
• [Presentation] (2008)
  • Author(s): 平木 彰
  • Organizer: 第25回代数的組合せ論研究集会
  • Place of Presentation: 北海道大学
  • Year and Date: 2008-06-23
• [Presentation] Fourth Korea-Japan Workshop on Algebra and Combinatorics (2008)
  • Author(s): A. HIRAKI
  • Place of Presentation: POSTECH
  • Year and Date: 2008-02-02
• [Presentation] (2007)
  • Author(s): 平木 彰
  • Organizer: 第24回代数的組合せ論研究集会
  • Place of Presentation: 近畿大学
  • Year and Date: 2007-06-30
• [Presentation] Albebraic Combinatrics (2006)
  • Author(s): A. HIRAKI
  • Organizer: An International Conference in Honour of Eiichi Bannai's 60th birthday
  • Place of Presentation: Sendai International Center
  • Year and Date: 2006-06-26
• [Remarks] 大阪教育大学リポジトリ
  • URL: http://ir.lib.osaka-kyoiku.ac.jp/dspace/