1999 Fiscal Year Final Research Report Summary
On relations between upper bound graphs and graph operations
| Project/Area Number |
10640135
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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 | Tokai University |
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Principal Investigator |
TSUCHIYA Morimasa Tokai University, School of Science, Associate Professor, 理学部, 助教授 (00188583)
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| Co-Investigator(Kenkyū-buntansha) |
MATSUMOTO Satoshi Tokai University, School of Science, Assistant Professor, 理学部, 講師 (30307235)
MATSUI Yasuko Tokai University, School of Science, Assistant Professor, 理学部, 講師 (10264582)
HARA Masao Tokai University, School of Science, Associate Professor, 理学部, 助教授 (10238165)
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| Project Period (FY) |
1998 – 1999
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| Keywords | graph theory / intersection graph / upper bound graph / graph operation |
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| Research Abstract |
We consider upper bound graphs with respect to operations on graphs. Using a concept of edge clique covers, we deal with characterizations of upper bound graphs obtained by graph operations of upper bound graphs. For example, for upper bound graphs G and H with |V(G)|【greater than or equal】2 and |V(H)|【greater than or equal】2, the composition G[H] is an upper bound graph if and only if H is a complete graph, and the square of an upper bound graph G is an upper bound graph if and only if the intersection graph of the corresponding edge clique cover of G is an upper bound graph.
We consider transformations between posets P and Q, whose upper baud graphs are the same. We obtain that P can be transformed into Q by a finite sequence of two transformations, that is, additions and deletions on posets. Furthermore we show some properties on minimum posets and maximal posets whose upper bound graphs are the same. We determine the maximum distance of posets.
Similarly we also consider double bound graphs on transformations and distances.
Next we deal with semi bound graphs. For a poset P, a graph G is a semi bound graph of P if V(G)=V(P) and μ,υεE(G) if and only if there exists a common upper bound of μ and υ or a common lower bound of μ and υ. We characterize semi bound graphs using properties on double bound graphs, and have another characterization of semi bound graphs in terms of clique covers.
We obtain some results on construction of upper bound graphs and double bound graphs. These results induce other characterizations on upper bound graphs and double bound graphs.
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