论文信息 - Bartholdi zeta functions of graph bundles having regular fibers

Bartholdi zeta functions of graph bundles having regular fibers

As a continuation of computing the Bartholdi zeta function of a regular covering of a graph by Mizuno and Sato in J. Combin. Theory Ser. B 89 (2003) 27, we derive in this paper some computational formulae for the Bartholdi zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the fiber is a Schreier graph or it is regular and the voltages to derive the bundle or the covering lie in an Abelian group, then the formulae can be simplified. As a byproduct, the Bartholdi zeta functions of Schreier graphs, Cayley graphs and the cartesian product of a graph and a regular graph are obtained.

Jin Ho Kwak | Moo Young Sohn | Jaeun Lee

[1] H. Bass. THE IHARA-SELBERG ZETA FUNCTION OF A TREE LATTICE , 1992 .

[2] Iwao Sato,et al. Zeta Functions of Graph Coverings , 2000, J. Comb. Theory, Ser. B.

[3] T. Sunada. L-functions in geometry and some applications , 1986 .

[4] L. Bartholdi. Counting Paths in Graphs , 2000, math/0012161.

[5] Audrey Terras. Fourier Analysis on Finite Groups and Applications: The Quadratic Reciprocity Law , 1999 .

[6] Norman Biggs. Algebraic Graph Theory: Index , 1974 .

[7] Jean-Pierre Serre,et al. Linear representations of finite groups , 1977, Graduate texts in mathematics.

[8] Y. Ihara. On discrete subgroups of the two by two projective linear group over p-adic fields , 1966 .

[9] J. Kwak,et al. Isomorphism Classes of Graph Bundles , 1990, Canadian Journal of Mathematics.

[10] K. Hashimoto. Zeta functions of finite graphs and representations of p-adic groups , 1989 .

[11] A. Terras,et al. Zeta functions of finite graphs and coverings, III , 1996 .

[12] Sam Northshield,et al. A Note on the Zeta Function of a Graph , 1998, J. Comb. Theory, Ser. B.

[13] Jonathan L. Gross,et al. Topological Graph Theory , 1987, Handbook of Graph Theory.

[14] Jin Ho Kwak,et al. Caracteristics polynomials of some grap bundlesII , 1992 .

[15] Iwao Sato,et al. Bartholdi zeta functions of graph coverings , 2003, J. Comb. Theory B.

[16] Michael Doob,et al. Spectra of graphs , 1980 .