Bartholdi zeta functions of graph bundles having regular fibers

  • Authors:

  • Jin Ho Kwak;Jaeun Lee;Moo Young Sohn

  • Affiliations:

  • Mathematics, Pohang University of Science and Technology, Pohang 790-784, Republic of Korea;Mathematics, Yeungnam University, Kyongsan 712-749, Republic of Korea;Applied Mathematics, Changwon National University, Changwon 641-773, Republic of Korea

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2005

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Abstract

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.