English

Generalized characteristic polynomials of graph bundles

Combinatorics 2008-07-03 v1

Abstract

In this paper, we find computational formulae for generalized characteristic polynomials of graph bundles. We show that the number of spanning trees in a graph is the partial derivative (at (0,1)) of the generalized characteristic polynomial of the graph. Since the reciprocal of the Bartholdi zeta function of a graph can be derived from the generalized characteristic polynomial of a graph, consequently, the Bartholdi zeta function of a graph bundle can be computed by using our computational formulae.

Keywords

Cite

@article{arxiv.0704.1431,
  title  = {Generalized characteristic polynomials of graph bundles},
  author = {Dongseok Kim and Hye Kyung Kim and Jaeun Lee},
  journal= {arXiv preprint arXiv:0704.1431},
  year   = {2008}
}