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arXiv · 0704.1431

Generalized characteristic polynomials of graph bundles

Dongseok Kim·Hye Kyung Kim·Jaeun Lee
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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.

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Dongseok Kim, Hye Kyung Kim, Jaeun Lee. 2007-04-11. Generalized characteristic polynomials of graph bundles. https://doi.org/10.1016/j.laa.2008.03.023

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