Double Covers of Flower Graphs and Tutte Polynomials
Kaustubh Verma
University of Minnesota
Abstract
When one has a double covering G' of G, it is known that the number of spanning trees for the base graph G divides the number for the cover G'. For a special class of graphs F that we will call flower graphs and their double coverings F', we generalize this divisibility by showing that the Tutte polynomial evaluation T_{F} (x, 1) divides T_{F'} (x, 1), and interpret the resulting quotient as a sum over negative vector felds on F.
