A generalized Bartholdi zeta function for a general graph

Abstract

We define an -variable Bartholdi zeta function and an -variable Bartholdi -function of a graph , and give determinant expressions of them. We present a decomposition formula for the -variable Bartholdi zeta function of a regular covering of . Furthermore, we express the -variable Bartholdi zeta function of a regular covering of G as a product of its -variable Bartholdi L-functions.

Keywords:

• zeta function
• graph covering

AMS Subject Classifications:

• 05C50
• 15A15

Acknowledgements

We would like to thank the referee for many valuable comments and many helpful suggestions.

Notes

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The first author was partially supported by Grant-in-Aid for Science Research (C) 15K04985.