2006 Fiscal Year Final Research Report Summary
Systematization of graph operations for interconnection networks and its application to fault diagnosis
| Project/Area Number |
16500006
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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 |
Fundamental theory of informatics
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| Research Institution | Gunma University |
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Principal Investigator |
SHIBATA Yukio GUNMA UNIVERSITY, Faculty of Engineering, Professor, 工学部, 教授 (80008531)
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| Project Period (FY) |
2004 – 2006
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| Keywords | de Brujin graph / Kautz graph / hypercube / feedback vertex set / interconnection network graph |
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| Research Abstract |
We have investigated feedback vertex set, decomposition, bookembedding, Cayley graph representation, enumeration and fault diagnosis mainly on graphs of de Bruijn family and hypercubes.
1. On the feedback vertex set problem, we have shown that for trivalent Cayley graphs and cube-connected cycles, there exist minimum feedback vertex sets with the order that are the same as the general lower bound for general graphs. For binary de Bruijn graph, we have shown that there exist examples such that the order of the minimum feedback vertex set is larger than the lower bound for general graphs. This suggests that there might be a interesting problem on the minimum feedback vertex set problem on nonbinary de Bruijn graphs.
2. On the Cayley graph representation, we have shown the group action graph representation of Kautz digraphs and the Cayley graph representation of dihedral butterflies. The group action graph representation of Kautz digraph is known as an unsolved problem and it is largely meaningful that the problem has been settled.
3. On the symmetry of graphs of variants of the hypercube, we have shown that some of variants of the hypercube are not vertex transitive.
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