2010/09/16 by Joanna A. Ellis-Monaghan, Criel Merino · 1 citation
Mathematics · Computer Science · #Graph theory and applications #Advanced Graph Theory Research #Advanced Combinatorial Mathematics #Tutte polynomial #Chromatic polynomial #Combinatorics #Mathematics #Discrete mathematics #Graph property #Algebraic graph theory #Integral graph #Graph #Voltage graph #Line graph
paper · doi:10.1007/978-0-8176-4789-6_9
openalex publication_date 2010/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04
In this survey of graph polynomials, we emphasize the Tutte polynomial and a selection of closely related graph polynomials such as the chromatic, flow, reliability, and shelling polynomials. We explore some of the Tutte polynomial’s many properties and applications and we use the Tutte polynomial to showcase a variety of principles and techniques for graph polynomials in general. These include several ways in which a graph polynomial may be defined and methods for extracting combinatorial information and algebraic properties from a graph polynomial. We also use the Tutte polynomial to demonstrate how graph polynomials may be both specialized and generalized, and how they can encode information relevant to physical applications. We conclude with a brief discussion of computational complexity considerations.