2001 Fiscal Year Final Research Report Summary
On bound graphs and cique covers
| Project/Area Number |
12640141
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | TOKAI UNIVERSITY |
|---|
Principal Investigator |
TUCHIYA Morimasa School of Science, Tokai University, Professor, 理学部, 教授 (00188583)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
MATSUMOTO Satoshi Schol of Scinece, Tokai University, Assistant Professor, 理学部, 講師 (30307235)
MATSUI Yasuko Schol of Scinece, Tokai University, Assistant Professor, 理学部, 講師 (10264582)
HARA Masao School of Science, Tokai University, Associate Professor, 理学部, 助教授 (10238165)
|
|---|
| Project Period (FY) |
2000 – 2001
|
| Keywords | graph theory / poset / upper bound graph / double bound graph / semi bound graph |
|---|
| Research Abstract |
We consider upper bound graphs and double bound graphs in terms of clique covers, intervals and order ideals. Using properties on intervals, we consider transformations between posets P and Q, whose double bound graphs are the same. We obtain that P can be transformed into Q by a finite sequence of two transformations, that is, d-additions and d-diletions. Furthermore we show some properties on minimal posets and maximum posets whose double bound graphs are the same. We determine the maximum distance of those posets. We also obtain properties of unique double bound graphs.
We deal with characterizations of double bound graphs obtained by graph operations (for example, sum, middle graph, total graph, corona, Cartesian product, composition, normal product, conjunction) of double bound graphs.
Using a concept of vertex-clique matrices, we obtain some properties on non-maximal cliques corresponding to vertices. By these results, we obtain other characterizations on double bound graphs and semi bound graphs in terms of clique covers. We also consider a family of posets with the same semi bound graph. We get some properties on minimal posets and maximal posets with the same semi bound graphs. We determine the maximum distance of those posets. We also consider properties of posets on bound graphs and we have some results on posets in terms of graph theory.
|
