Structures and representations of distance-regular graphs

• Project/Area Number: 21540023
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: International Christian University
• Principal Investigator: SUZUKI HIROSHI 国際基督教大学, 教養学部, 教授 (10135767)
• Project Period (FY): 2009-04-01 – 2014-03-31
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 代数的組合せ論 / 距離正則グラフ / Terwilliger 代数 / 完全正則符号 / 有限幾何 / アソシエーションスキーム / グラフの表現 / 代数学 / Terwilliger代数

Research Abstract

Through the investigations of completely regular codes of a graph not necessarily distance-regular, I reached a concept of completely regular clique graphs, and gave several evidence that it plays a key role in a classification of classical distance-regular graphs. In particular, a thorough investigation of thin completely regular clique graphs will imply a classification of thin Q-polynomial distance-regular graphs.

Research Products

• [Journal Article] Completely Regular Clique Graphs (2014)
  • Author(s): Hiroshi Suzuki
  • Journal Title: Journal of Algebraic Combinatorics Volume: 印刷中 Issue: 1 Pages: 233-244
  • DOI: 10.1007/s10801-013-0485-2
  • Peer Reviewed
• [Journal Article] Edge-Distance-Regular Graphs (2013)
  • Author(s): M. Camara, C. Dalfo, C. Delorme, M. A. Fiol and H. Suzuki
  • Journal Title: Journal Combinatorial Theory, Series A Volume: 120
  • Peer Reviewed
• [Journal Article] Edge-distance-regular graphs are distance-regular (2013)
  • Author(s): Camara, M, Daflo, C, Delorme, C, Fiol, M A, Suzuki, H
  • Journal Title: Journal of Combinatorial Theory, Series A Volume: 120 Issue: 5 Pages: 1057-1067
  • DOI: 10.1016/j.jcta.2013.02.006
  • Peer Reviewed
• [Journal Article] Intriguing Sets of Vertices of Regular Graphs (2010)
  • Author(s): B. De Bruyn, H. Suzuki
  • Journal Title: Graphs and Combinatorics Volume: 26
  • Peer Reviewed
• [Journal Article] Intriguing sets of vertices of regular graphs (2010)
  • Author(s): Bart De Bruyn, Hiroshi Suzuki
  • Journal Title: Graphs and Combinatorics Volume: 26 Pages: 629-646
  • Peer Reviewed
• [Journal Article] Non-existence of Imprimitive Q-polynomial Schemes of Exceptional Type with d =4 (2009)
  • Author(s): D. Cerzo, and H. Suzuki
  • Journal Title: European Journal of Combinatorics Volume: 30 Pages: 674-681
  • Peer Reviewed
• [Journal Article] Parallelogram-Free Distance-Regular Graphs Having Completely Regular Strongly Regular Subgraphs (2009)
  • Author(s): H. Suzuki
  • Journal Title: Journal of Algebraic Combinatorics Volume: 30 Pages: 401-413
  • Peer Reviewed
• [Journal Article] Completely Regular Clique Graph
  • Author(s): H. Suzuki
  • Journal Title: Journal of Algebraic Combinatorics Volume: (to appear)
  • Peer Reviewed
• [Journal Article] Intriguing sets of vertices of regular graphs
  • Author(s): Bart De Bruyn
  • Journal Title: Graphs and Combinatorics (印刷中)
  • Peer Reviewed
• [Presentation] Completely Regular Clique Graphs and Thin Distance-Regular Graphs (2014)
  • Author(s): H. Suzuki
  • Organizer: 代数的組合せ論ミニ集会
  • Place of Presentation: 神戸学院大学ポートアイランドキャンパス
  • Year and Date: 2014-03-07
• [Presentation] Edge-distance-regular graphs are distance-regular (2012)
  • Author(s): H. Suzuki
  • Organizer: 2012 Shanghai Conference on Algebraic Combinatorics
  • Place of Presentation: Shanghai Jiao Tong University
  • Year and Date: 2012-08-21
• [Presentation] On Representation Diagrams of a Distance-Regular Graph (2010)
  • Author(s): H. Suzuki
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: 河北師範大学(中国)
  • Year and Date: 2010-11-27
• [Presentation] On representation diagrams of a distance-regular graph (2010)
  • Author(s): Suzuki, Hiroshi
  • Organizer: Workshop on Algebraic Combinatorics
  • Place of Presentation: 河北師範大学(中国)(招待講演)
  • Year and Date: 2010-11-27
• [Presentation] The Terwilliger Algebra of a Polynomial Space (2009)
  • Author(s): H. Suzuki
  • Organizer: 22nd British Combinatorial Conference
  • Place of Presentation: University of St. Andrews, U.K
  • Year and Date: 2009-07-07
• [Presentation] The Terwilliger Algebra of a Polynomial Space (2009)
  • Author(s): Hiroshi Suzuki
  • Organizer: 22bd British Combinatorial Conference
  • Place of Presentation: Univ.St.Andrews, U.K.
  • Year and Date: 2009-07-07
• [Presentation] Distance-Regular Graphs Having Certain Completely Regular Subgraphs (2009)
  • Author(s): H. Suzuki
  • Organizer: American Mathematical Society, 2009, Spring Eastern Section Meeting
  • Place of Presentation: Worcester, MA, U.S.A
  • Year and Date: 2009-04-26
• [Presentation] Distance-Regular Graphs Having Certain Completely Regular Subgraphs (2009)
  • Author(s): Hiroshi Suzuki
  • Organizer: American Mathematical Society, 2009, Spring Eastern Section Meeting
  • Place of Presentation: Worcester, MA, U.S.A.
  • Year and Date: 2009-04-26
• [Presentation] Completely Regular Clique Graphs and Thin Distance-Regular Graphs
  • Author(s): Hiroshi Suzuki
  • Organizer: 代数的組合せ論ミニ集会
  • Place of Presentation: 神戸学院大学ポートアイランドキャンパス
• [Remarks]
  • URL: http://subsite.icu.ac.jp/people/hsuzuki/
• [Remarks] Suzuki's Home Page
  • URL: http://subsite.icu.ac.jp/people/hsuzuki/