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Graph Polynomials and Their Applications II: Interrelations and Interpretations

In: Structural Analysis of Complex Networks

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  • Joanna A. Ellis-Monaghan

    (Saint Michaels College, Department of Mathematics
    University of Vermont, Department of Mathematics and Statistics)

  • Criel Merino

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.

Suggested Citation

  • Joanna A. Ellis-Monaghan & Criel Merino, 2011. "Graph Polynomials and Their Applications II: Interrelations and Interpretations," Springer Books, in: Matthias Dehmer (ed.), Structural Analysis of Complex Networks, chapter 0, pages 257-292, Springer.
    • Handle: RePEc:spr:sprchp:978-0-8176-4789-6_10
    DOI: 10.1007/978-0-8176-4789-6_10
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