Graph Coverings and Their Generalization
Project/Area Number  07640342 
Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear 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 ; gcyclic Acovers. We study three enumerations in this repot. The general problem of counting the ismorphism classes of regular nfold 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 GAMMAisomorphism classes of regular 4fold coverings of G is a narural problem. A regular 4fold covering of G is either a Z_2*Z_2covering or a Z_4covering of G.We enumerate the GAMMAisomorphism classes of Z_2*Z_2coverings 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 gcyclic Acover 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 gcyclic Acovers of D to be ismorphic with respect to a group GAMMA of automorphisms of D.Thus, we enumerate the Iisomophism classes of gcyclic Z_<pn>covers of D for any p (>2). Furthermore, we count the GAMMAisomophism classes of gcyclic Z_pcovers of D. Related to connected gcyclic acovers, we present a decomposition formula for the number of Iisomorphism classes of gcyclic Acovers 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 Iisomorphism classes of gcyclic Acovers 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
(4results)
Research Output
(18results)