J. Korean Math. Soc. 2006; 43(6): 1269-1287
Printed November 1, 2006
Copyright © The Korean Mathematical Society.
Rongquan Feng and Jin Ho Kwak
Peking University, Pohang University of Science and Technology
As a continuation of computing the zeta function of a regular covering graph by Mizuno and Sato in [9], we derive in this paper computational formulae for the zeta functions of a graph bundle and of any (regular or irregular) covering of a graph. If the voltages to derive them lie in an abelian or dihedral group and its fibre is a regular graph, those formulae can be simplified. As a by-product, the zeta function of the cartesian product of a graph and a regular graph is obtained. The same work is also done for a discrete torus and for a discrete Klein bottle.
Keywords: zeta function, graph bundle, voltage assignment, discrete torus or Klein bottle
MSC numbers: 05C50, 05C25, 15A15, 15A18
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