Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ZETA FUNCTIONS OF GRAPH BUNDLES

  • Feng, Rongquan (LMAM, School of Mathematical Sciences Peking University) ;
  • Kwak, Jin-Ho (Department of Mathematics Pohang University of Science and Technology)
  • Published : 2006.11.01
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Abstract

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.

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References

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  1. Zeta functions of infinite graph bundles vol.58, pp.2, 2010, https://doi.org/10.1080/03081080801928084
  2. Bartholdi zeta and L-functions of weighted digraphs, their coverings and products vol.213, pp.2, 2007, https://doi.org/10.1016/j.aim.2007.01.013