Configurations from a Graphical Viewpoint

  • Tomaž Pisanski
  • Brigitte Servatius

Part of the Birkhäuser Advanced Texts Basler Lehrbücher book series (BAT)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Tomaž Pisanski, Brigitte Servatius
    Pages 1-14
  3. Tomaž Pisanski, Brigitte Servatius
    Pages 15-53
  4. Tomaž Pisanski, Brigitte Servatius
    Pages 55-103
  5. Tomaž Pisanski, Brigitte Servatius
    Pages 105-155
  6. Tomaž Pisanski, Brigitte Servatius
    Pages 157-196
  7. Tomaž Pisanski, Brigitte Servatius
    Pages 197-263
  8. Back Matter
    Pages 265-279

About this book

Introduction

Configurations can be studied from a graph-theoretical viewpoint via the so-called Levi graphs and lie at the heart of graphs, groups, surfaces, and geometries, all of which are very active areas of mathematical exploration. In this self-contained textbook, algebraic graph theory is used to introduce groups; topological graph theory is used to explore surfaces; and geometric graph theory is implemented to analyze incidence geometries.

After a preview of configurations in Chapter 1, a concise introduction to graph theory is presented in Chapter 2, followed by a geometric introduction to groups in Chapter 3. Maps and surfaces are combinatorially treated in Chapter 4. Chapter 5 introduces the concept of incidence structure through vertex colored graphs, and the combinatorial aspects of classical configurations are studied. Geometric aspects, some historical remarks, references, and applications of classical configurations appear in the last chapter.

With over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems, Configurations from a Graphical Viewpoint is well suited for a graduate graph theory course, an advanced undergraduate seminar, or a self-contained reference for mathematicians and researchers.

Keywords

Cayley graphs Escher problem Kronecker cover The Steinitz theorem Voltage graphs dipoles or theta graphs incidence geometries incidence structures polycyclic configurations vertex splitting

Authors and affiliations

  • Tomaž Pisanski
    • 1
  • Brigitte Servatius
    • 2
  1. 1.Oddelek za Teoretično Racunalništvo, Univerza v LjubljaniIMFMLjubljanaSlovenia
  2. 2.Worcester Polytechnic InstituteMathematics DepartmentWorcesterUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-8176-8364-1
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Birkhäuser, Boston
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-8176-8363-4
  • Online ISBN 978-0-8176-8364-1
  • About this book