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Abstract: In this survey of graph polynomials, we emphasize the Tutte polynomial and aselection of closely related graph polynomials. We explore some of the Tuttepolynomial-s many properties and applications and we use the Tutte polynomialto showcase a variety of principles and techniques for graph polynomials ingeneral. These include several ways in which a graph polynomial may be definedand methods for extracting combinatorial information and algebraic propertiesfrom a graph polynomial. We also use the Tutte polynomial to demonstrate howgraph polynomials may be both specialized and generalized, and how they canencode information relevant to physical applications. We conclude with a briefdiscussion of computational complexity considerations.



Author: Joanna Ellis-Monaghan, Criel Merino

Source: https://arxiv.org/







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