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Research on the enumeration of graphs

Research Project

Project/Area Number 22540160
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionKinki University

Principal Investigator

TAZAWA Shinsei  近畿大学, 総合社会学部, 教授 (80098657)

Co-Investigator(Kenkyū-buntansha) ASAI Tsunenobu  近畿大学, 理工学部, 准教授 (70257963)
OHNO Yasuo  近畿大学, 理工学部, 教授 (70330230)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsグラフ / 標識自己補グラフ / 数え上げ / 母関数 / 自己補2部グラフ
Research Abstract

We have studied intensively the enumeration of selfcomplementary graphs. In 1973, Harary and Palmer announced an enumeration problem of labeled selfcomplementary graphs at the end of their book (Graphical Enumeration, Academic Press, New York and London, 1973). This research from April, 2010 to March, 2013 gave an answer of this problem. Moreover, this research gave following formulas: (1) A formula on the number of labeled selfcomplementary graphs with the given order of automorphism groups and (2) A formula on the number of unlabeled selfcomplementary graphs with the given order of automorphism groups of those graphs. This result will be appeared in "Utilitas Mathematica".

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (23 results)

All 2013 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (18 results) (of which Invited: 1 results)

  • [Journal Article] 標識偶ブロックの数え上げについて2012

    • Author(s)
      田澤新成
    • Journal Title

      近畿大学総合社会学部紀要

      Volume: Vol.1, No.2 Pages: 19-23

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] 標識グラフの数え上げ問題についての一考察2011

    • Author(s)
      田澤新成
    • Journal Title

      近畿大学総合社会学部紀要

      Volume: Vol.1, No.1 Pages: 49-53

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Enumeration of bipartite self-comple- mentary graphs

    • Author(s)
      Makoto Ueno and Shinsei Tazawa
    • Journal Title

      Graphs and Combina -torics

      Volume: (掲載確定)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The enumeration of labelled self-complementary graphs

    • Author(s)
      Shinsei Tazawa
    • Journal Title

      Utilitas Mathematica(掲載確定)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Edge colored complete graphs and a generalization of self complementarity

    • Author(s)
      Kumi Kobata and Yasuo Ohno
    • Journal Title

      Utilitas Mathematica(掲載確定)

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] 母関数とグラフの数え上げ2013

    • Author(s)
      田澤新成
    • Organizer
      第9回組合せ論若手研究集会(招待講演)
    • Place of Presentation
      慶應義塾大学
    • Year and Date
      2013-03-16
    • Related Report
      2012 Final Research Report
  • [Presentation] On enumeration of edge colored graphs2013

    • Author(s)
      Kumi Kobata and Yasuo Ohno
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学 数学研究所
    • Year and Date
      2013-02-01
    • Related Report
      2012 Final Research Report
  • [Presentation] 有限群の p-部分群と斜準同型写像について2013

    • Author(s)
      淺井恒信、庭崎隆
    • Organizer
      RIMS研究集会「有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2013-01-10
    • Related Report
      2012 Final Research Report
  • [Presentation] On the enumeration of certain edge-colored graphs2012

    • Author(s)
      大野泰生
    • Organizer
      RIMS研究集会「有限群とその表現、頂点作用素代数、組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2012-03-07
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] A generalization of an enumeration on cyclic automorphism graphs for edge colored hypergraphs2012

    • Author(s)
      小畑久美、大野泰生
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学数学研究所
    • Year and Date
      2012-02-03
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] Riddell型方程式について2011

    • Author(s)
      田澤新成
    • Organizer
      研究集会「数え上げについての種々の問題およびその周辺」
    • Place of Presentation
      島根大学(島根県)
    • Year and Date
      2011-11-02
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] グラフのインデックスを利用してのグラフの描き方について2011

    • Author(s)
      田澤新成
    • Organizer
      研究集会「数え上げについての種々の問題およびその周辺」
    • Place of Presentation
      島根大学(島根県)
    • Year and Date
      2011-11-02
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] 標識自己補2部グラフの数え上げについて2011

    • Author(s)
      菱岡由衣、田澤新成
    • Organizer
      研究集会「数え上げについての種々の問題およびその周辺」
    • Place of Presentation
      島根大学(島根県)
    • Year and Date
      2011-11-02
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] 辺着色hypergraphにおける巡回自己同型について2011

    • Author(s)
      小畑久美、大野泰生
    • Organizer
      日本数学会・秋季総合分科会・応用数学分科会
    • Place of Presentation
      信州大学(長野県)
    • Year and Date
      2011-09-28
    • Related Report
      2012 Final Research Report 2011 Annual Research Report
  • [Presentation] 辺着色有向グラフと巡回自己同型2011

    • Author(s)
      小畑久美、大野泰生
    • Organizer
      日本数学会・年会・応用数学分科会
    • Place of Presentation
      早稲田大学(東京都)
    • Year and Date
      2011-03-20
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] A generalization of an enumeration on self-complementary graphs for edge colored bipartite graphs2010

    • Author(s)
      小畑久美、大野泰生
    • Organizer
      2010年度応用数学合同研究集会
    • Place of Presentation
      龍谷大学(滋賀県)
    • Year and Date
      2010-12-17
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] 標識自己補グラフの数え上げの考察2010

    • Author(s)
      田澤新成
    • Organizer
      研究集会「数え上げの問題とその周辺」
    • Place of Presentation
      鹿児島大学(鹿児島県)
    • Year and Date
      2010-10-29
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] 2部グラフの数え上げ問題の考察2010

    • Author(s)
      田澤新成
    • Organizer
      研究集会「数え上げの問題とその周辺」
    • Place of Presentation
      鹿児島大学(鹿児島県)
    • Year and Date
      2010-10-29
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] 辺着色2部グラフの巡回自己同型について2010

    • Author(s)
      小畑久美、大野泰生
    • Organizer
      日本数学会・秋季総合分科会・応用数学分科会
    • Place of Presentation
      名古屋大学(愛知県)
    • Year and Date
      2010-09-22
    • Related Report
      2012 Final Research Report 2010 Annual Research Report
  • [Presentation] 母関数とグラフの数え上げ

    • Author(s)
      田澤新成
    • Organizer
      第9回組合せ論若手研究集会
    • Place of Presentation
      慶応義塾大学
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] On enumeration of edge colored graphs

    • Author(s)
      Kumi Kobata・ Yasuo Ohno
    • Organizer
      Friday Seminar on Knot Theory
    • Place of Presentation
      大阪市立大学 数学研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] 有限群の p-部分群と斜準同型写像について

    • Author(s)
      淺井恒信・庭崎隆
    • Organizer
      RIMS研究集会「有限群とその表現, 頂点作用素代数, 代数的組合せ論の研究」
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Annual Research Report
  • [Presentation] Riddle型方程式の活用について

    • Author(s)
      田澤新成
    • Organizer
      山崎洋平先生ご退職記念研究集会
    • Place of Presentation
      近畿大学(東大阪市)
    • Related Report
      2012 Annual Research Report

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Published: 2010-08-23   Modified: 2019-07-29  

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