Generalized characteristic polynomials of graph bundles

Details Generalized characteristic polynomials of graph bundles Generalized characteristic polynomials of graph bundles

2007-04-11

arxiv.org/abs/0704.1431v1

Linear Algebra and its Applications 429 (2008) 688--697

Mathematics

Combinatorics

Scientific paper

10.1016/j.laa.2008.03.023

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.

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