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 coveringsĀ  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.

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Dates
Published: 2021-07-06
How to Cite
Verma, K. (2021). Double Covers of Flower Graphs and Tutte Polynomials. Minnesota Journal of Undergraduate Mathematics, 6(1). Retrieved from https://pubs.lib.umn.edu/index.php/mjum/article/view/4267
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