Graph Coverings and Their Generalization
| Project/Area Number |
07640342
|
|---|
| 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 | Oyama National College of Technology |
|---|
Principal Investigator |
SATO Iwao Oyama National college of Technology, Associate Professor, 助教授 (70154036)
|
|---|
| Project Period (FY) |
1995 – 1997
|
| Project Status |
Completed (Fiscal Year 1997)
|
| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1997: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1996: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 1995: ¥900,000 (Direct Cost: ¥900,000)
|
|---|
| Keywords | graph covering / enumeration |
|---|
| Research Abstract |
We consider two objects in graph coverings and their generalization : regular coverings ; g-cyclic A-covers. We study three enumerations in this repot.
The general problem of counting the ismorphism classes of regular n-fold coverings of a graph G with respect to a group GAMMA of automorphisms of G is still unsolved except in the case that n is prime. The enumeration of GAMMA-isomorphism classes of regular 4-fold coverings of G is a narural problem. A regular 4-fold covering of G is either a Z_2*Z_2-covering or a Z_4-covering of G.We enumerate the GAMMA-isomorphism classes of Z_2*Z_2-coverings of a connected graph.
Next, for a connected symmetric digraph D,a finite group A and g<not a member of>A,we introduce a g-cyclic A-cover of D as a generalization of a regular covering of a graph. In the case that A is an abelian group with some property and the order of g is odd, we present a characterization for two g-cyclic A-covers of D to be ismorphic with respect to a group GAMMA of automorphisms of D.Thus, we enumerate the I-isomophism classes of g-cyclic Z_<pn>-covers of D for any p (>2). Furthermore, we count the GAMMA-isomophism classes of g-cyclic Z_p-covers of D.
Related to connected g-cyclic a-covers, we present a decomposition formula for the number of I-isomorphism classes of g-cyclic A-covers of a connected symmetric digraph D for any finite abelian group A and any g<not a member of>A of odd order. Furthermore, we enumerate the I-isomorphism classes of g-cyclic A-covers of D,when A is the cyclic group Z_<pn> and the direct sum of m copies of Z_p for any prime number p (>2).
|
Report
(4 results)
Research Products
(18 results)
