Graphs on Surfaces

Dualities, Polynomials, and Knots

  • Joanna A. Ellis-Monaghan
  • Iain Moffatt

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Joanna A. Ellis-Monaghan, Iain Moffatt
    Pages 1-22
  3. Joanna A. Ellis-Monaghan, Iain Moffatt
    Pages 23-42
  4. Joanna A. Ellis-Monaghan, Iain Moffatt
    Pages 43-60
  5. Joanna A. Ellis-Monaghan, Iain Moffatt
    Pages 61-99
  6. Joanna A. Ellis-Monaghan, Iain Moffatt
    Pages 101-131
  7. Back Matter
    Pages 133-139

About this book

Introduction

Graphs on Surfaces: Dualities, Polynomials, and Knots offers an accessible and comprehensive treatment of recent developments on generalized duals of graphs on surfaces, and their applications. The authors  illustrate the interdependency between duality, medial graphs and knots; how this interdependency is reflected in algebraic invariants of graphs and knots; and how it can be exploited to solve problems in graph and knot theory. Taking  a constructive approach, the authors emphasize how generalized duals and related ideas arise by localizing classical constructions, such as geometric duals and Tait graphs, and then removing artificial restrictions in these constructions to obtain full extensions of them to embedded graphs. The authors demonstrate the benefits of these generalizations to embedded graphs in chapters describing their applications to graph polynomials and knots.  

 Graphs on Surfaces: Dualities, Polynomials, and Knots  also provides a self-contained introduction to graphs on surfaces, generalized duals, topological graph polynomials, and knot polynomials that is accessible both to graph theorists and to knot theorists.  Directed at those with some familiarity with basic graph theory and knot theory, this book is appropriate for graduate students and researchers in either area. Because the area is advancing so rapidly, the authors give a comprehensive overview of the topic and include a robust bibliography, aiming to provide the reader with the necessary foundations to stay abreast of the field. The reader will come away from the text convinced of advantages of considering these higher genus analogues of constructions of plane and abstract graphs, and with a good understanding of how they arise.

Keywords

Embedded Graphs Partial Duality Penrose Polynomial Ribbon Graph Tutte Polynomial Twisted Duality

Authors and affiliations

  • Joanna A. Ellis-Monaghan
    • 1
  • Iain Moffatt
    • 2
  1. 1.Dept. of MathematicsSaint Michael's CollegeColchesterUSA
  2. 2.Royal Holloway, Department of MathematicsUniversity of LondonSurreyUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-6971-1
  • Copyright Information Joanna A. Ellis-Monaghan, Iain Moffatt 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-6970-4
  • Online ISBN 978-1-4614-6971-1
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book