BARTHOLDI ZETA AND L-FUNCTIONS OF WEIGHTED DIGRAPHS, THEIR COVERINGS AND PRODUCTS
- BARTHOLDI ZETA AND L-FUNCTIONS OF WEIGHTED DIGRAPHS, THEIR COVERINGS AND PRODUCTS
- Choe, YB; Kwak, JH; Park, YS; Sato, I
- Date Issued
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Since a zeta function of a regular graph was introduced by Ihara [Y. Ihara, On discrete subgroups of the two by two projective linear group over rho-adic fields, J. Math. Soc. Japan 19 (1966) 219-235], many kinds of zeta functions and L-functions of a graph or a digraph have been defined and investigated. Most of the works concerning zeta and L-functions of a graph contain the following: (1) defining a zeta function, (2) defining an L-function associated with a (regular) graph covering, (3) providing their determinant expressions, and (4) computing the zeta function of a graph covering and obtaining its decomposition formula as a product of L-functions. As a continuation of those works, we introduce a zeta function of a weighted digraph and an L-function associated with a weighted digraph bundle. A graph bundle is a notion containing a cartesian product of graphs and a (regular or irregular) graph covering. Also we provide determinant expressions of the zeta function and the L-function. Moreover, we compute the zeta function of a weighted digraph bundle and obtain its decomposition formula as a product of the L-functions. (c) 2007 Elsevier Inc. All rights reserved.
- Article Type
- ADVANCES IN MATHEMATICS, vol. 213, no. 2, page. 865 - 886, 2007-08-20
- Files in This Item:
- There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.