| Project/Area Number |
15540143
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kinki University |
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Principal Investigator |
TAZAWA Shinsei Kinki University, School of Science and Engineering, Professor, 理工学部, 教授 (80098657)
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| Co-Investigator(Kenkyū-buntansha) |
ASAI Tsunenobu Kinki University, School of Science and Engineering, Associate professor, 理工学部, 助教授 (70257963)
NAKAMOTO Atsuhiro Yokohama National University, Faculty of Education and Human Sciences, Associate professor, 教育人間科学部, 助教授 (20314445)
OHNO Yasuo Kinki University, School of Science and Engineering, Associate professor, 理工学部, 助教授 (70330230)
SHIRAKURA Teruhiro Kobe University, Faculty of Human Development, Professor, 発達科学部, 教授 (30033913)
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| Project Period (FY) |
2003 – 2005
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| Project Status |
Completed (Fiscal Year 2005)
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| Budget Amount *help |
¥2,200,000 (Direct Cost: ¥2,200,000)
Fiscal Year 2005: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2004: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2003: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Graph / Self-complementary graph / Enumeration / Permutation group / Automorphism group / 2部グラフ |
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| Research Abstract |
We have studied intensively the enumeration of self-complementary graphs. Until now, the enumeration of unlabeled self-complementary graphs has been studied by R.C.Read in 1963 and has been, after that, by many researchers. The self-complementary graphs is defined as follows : The complement, G__-, of a graph G is the graph with vertex set V(G) such that two vertices are adjacent in G__- if and only if these vertices are not adjacent in G. G and G__- is self-complement if G and G__- are isomorphic. For a self-complementary graph G, we considered a set K(G) of isomorphisms from G to G__-. Let A(G) be the automorphism group of G. Then we found a relation between K(G) and A(G) which was announced at Shirahama in Wakayama prefecture on December 4, 2003. We have investigated this relation in detail and we found an important approach on the enumeration of labeled self-complementary graphs, which was announced in Okayama University of Science, September 22, 2005, and in Nagasaki University, January 6, 2006. K(G) is a subset of the union of conjugate classes of symmetry group on vertex set. We can list up all the labeled self-complementary graphs by way of K(G), but each of those are chosen many times. This is a difficult point in our research. We challenged ourselves to this difficult point and we got a result for the enumeration of self-complementary graphs of order eight, which was announced in Mathematical Society of Japan being held in Chuo University on February 26, 2006.
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