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On Characterisations and Classifications of graphs by their Eigenvalues

Research Project

Project/Area Number 16K05263
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

Taniguchi Tetsuji  広島工業大学, 工学部, 准教授 (90543728)

Co-Investigator(Kenkyū-buntansha) 宗政 昭弘  東北大学, 情報科学研究科, 教授 (50219862)
Project Period (FY) 2016-04-01 – 2020-03-31
Project Status Completed (Fiscal Year 2019)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Keywords代数的グラフ理論 / スペクトラルグラフ理論 / 代数的組合せ論 / 固有値 / 整格子 / グラフ / 格子 / 量子ウォーク / 離散数学
Outline of Final Research Achievements

In this project, we have been studying on the structure of a generalized Bethe tree and a Hoffman graph. The structure of a generalized Bethe tree is hierarchical and symmetric, but it is very difficult to see the eigenvalues. With Segawa, Kubota, and Yoshie, we obtained results on the periodicity of the Grover Walk in the class.
In addition, by generalizing the fat vertices and (signed) edges of a Hoffman graph, the Hoffman graph and generalized integral lattices can be associated. This makes it possible to explain the ingerability of generalized integral lattices. In problem of classifications of 3-lattices, we obtained the results that can be said to be the final goal on the line graph of the signed graph derived from integral lattices.

Academic Significance and Societal Importance of the Research Achievements

量子ウォークや整格子の分類・特徴付けは,量子コンピュータ,代数符号などの発展に貢献できる。
量子ウォークの周期性などは,量子探索などビッグデータの発展に寄与できる。また,グラフという構造は代数構造を詳細に表す言葉として重要である。ホフマングラフの一般化を得たことは,これまで整格子の構造の詳細を説明する道具がほとんどなかった中で,大きな成果と言ってよい。

Report

(5 results)
  • 2019 Annual Research Report   Final Research Report ( PDF )
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (25 results)

All 2019 2018 2017 2016 Other

All Int'l Joint Research (3 results) Journal Article (3 results) (of which Peer Reviewed: 3 results,  Open Access: 1 results) Presentation (17 results) (of which Int'l Joint Research: 2 results,  Invited: 5 results) Funded Workshop (2 results)

  • [Int'l Joint Research] 中国科学技術大学(中国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] 中国科学技術大学(中国)

    • Related Report
      2017 Research-status Report
  • [Int'l Joint Research] 中国科学技術大学(中国)

    • Related Report
      2016 Research-status Report
  • [Journal Article] A quantum walk induced by Hoffman graphs and its periodicity2019

    • Author(s)
      Kubota Sho、Segawa Etsuo、Taniguchi Tetsuji、Yoshie Yusuke
    • Journal Title

      Linear Algebra and its Applications

      Volume: 579 Pages: 217-236

    • DOI

      10.1016/j.laa.2019.05.026

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On graphs with the smallest eigenvalue at least -1-√2, part III2019

    • Author(s)
      Kubota Sho、Taniguchi Tetsuji、Yoshino Kiyoto
    • Journal Title

      Ars Mathematica Contemporanea

      Volume: 17 Issue: 2 Pages: 555-579

    • DOI

      10.26493/1855-3974.1581.b47

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Periodicity of Grover walks on generalized Bethe trees2018

    • Author(s)
      Sho Kubota, Etsuo Segawa, Tetsuji Taniguchi, Yusuke Yoshie
    • Journal Title

      Linear Algebra and its Applications

      Volume: 554 Pages: 371-391

    • DOI

      10.1016/j.laa.2018.05.023

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Presentation] generalized Hoffman Graph2019

    • Author(s)
      谷口哲至
    • Organizer
      博多ワークショップ
    • Related Report
      2019 Annual Research Report
  • [Presentation] weighted Hoffman Graph2019

    • Author(s)
      Tetsuji Taniguchi
    • Organizer
      9th Slovenian International Conference on Graph Theory - Bled'19
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Generalization of Hoffman Graph2019

    • Author(s)
      Tetsuji Taniguchi
    • Organizer
      Sendai Workshop on Combinatorics
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research
  • [Presentation] A Generalization of Hoffman Graph2019

    • Author(s)
      谷口哲至
    • Organizer
      2020組合せ論とその周辺研究集会
    • Related Report
      2019 Annual Research Report
  • [Presentation] スペクトラルグラフ理論研究における数学ソフトウェアの活用2019

    • Author(s)
      谷口哲至
    • Organizer
      松江セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] スペクトラルグラフ理論研究における数学ソフトウェアの活用2019

    • Author(s)
      谷口哲至
    • Organizer
      数学ソフトウェアとフリードキュメントXXVIII
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] ホフマングラフのその後2018

    • Author(s)
      谷口哲至
    • Organizer
      COS2018
    • Related Report
      2018 Research-status Report
  • [Presentation] グラフの固有値2018

    • Author(s)
      谷口哲至
    • Organizer
      松江セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] 一般べーテ木におけるグローバーウォークの周期性2017

    • Author(s)
      谷口哲至
    • Organizer
      第34回代数的組合せ論シンポジウム
    • Related Report
      2017 Research-status Report
  • [Presentation] 一般べーテ木におけるグローバーウォークの周期性2017

    • Author(s)
      谷口哲至
    • Organizer
      COS2017
    • Related Report
      2017 Research-status Report
  • [Presentation] グラフの固有値に対する禁止グラフ2017

    • Author(s)
      谷口哲至
    • Organizer
      応用数学合同研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] グラフの固有値に対する禁止グラフ2017

    • Author(s)
      谷口哲至
    • Organizer
      軽井沢グラフと解析研究集会
    • Related Report
      2017 Research-status Report
  • [Presentation] A Representation of Hoffman Graphs2017

    • Author(s)
      谷口哲至
    • Organizer
      代数・解析・幾何学セミナー
    • Place of Presentation
      鹿児島大学(鹿児島県鹿児島市)
    • Related Report
      2016 Research-status Report
  • [Presentation] ホフマングラフ2017

    • Author(s)
      谷口哲至
    • Organizer
      代数的組合せ論「仙台勉強会」
    • Place of Presentation
      東北大学(宮城県仙台市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] スターコンプリメントテクニックと最小固有値が-2以上のグラフの生成2016

    • Author(s)
      谷口哲至
    • Organizer
      Mathematicaを使った数学
    • Place of Presentation
      アルゴグラフィックス(東京都中央区)
    • Related Report
      2016 Research-status Report
  • [Presentation] あるグラフクラスタリングとグラフの最小固有値2016

    • Author(s)
      谷口哲至
    • Organizer
      組合せ論サマースクール
    • Place of Presentation
      下呂市民会館(岐阜県下呂市)
    • Related Report
      2016 Research-status Report
  • [Presentation] 辺符号グラフとホフマングラフ2016

    • Author(s)
      谷口哲至
    • Organizer
      名古屋組合せ論セミナー
    • Place of Presentation
      愛知県産業労働センター(愛知県名古屋市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Funded Workshop] The Japanese Conference on Combinatorics and its Applications (JCCA 2018)2018

    • Related Report
      2018 Research-status Report
  • [Funded Workshop] The Japanese conference on combinatorics and its applications2016

    • Place of Presentation
      京都大学(京都府京都市)
    • Year and Date
      2016-05-21
    • Related Report
      2016 Research-status Report

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Published: 2016-04-21   Modified: 2021-02-19  

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