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Graph Polynomials and Their Applications II: Interrelations and Interpretations

  • Joanna A. Ellis-Monaghan
  • Criel Merino
Chapter

Abstract

We survey a variety of graph polynomials, giving a brief overview of techniques for defining a graph polynomial and then for decoding the combinatorial information it contains. These polynomials are not generally specializations of the Tutte polynomial, but they are each in some way related to the Tutte polynomial, and often to one another. We emphasize these interrelations and explore how an understanding of one polynomial can guide research into others. We also discuss multivariable generalizations of some of these polynomials and the theory facilitated by this. We conclude with two examples, the interlace polynomial in biology and the Tutte polynomial and Potts model in physics, that illustrate the applicability of graph polynomials in other fields.

Keywords

Tutte polynomial Characteristic polynomial Matching polynomial Penrose polynomial Martin polynomial Circuit partition polynomial Ehrhart polynomial Interlace polynomial U-polynomial W-polynomial Bollobás–Riordan polynomial Ribbon graph polynomial Topological Tutte polynomial Multivariable Tutte polynomial Parametrized Tutte polynomial Transition polynomial Polychromate Symmetric function DNA sequencing Potts model 

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© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of MathematicsSaint Michaels CollegeColchesterUSA
  2. 2.Department of Mathematics and StatisticsUniversity of VermontBurlingtonUSA

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