Overview
- Among the oldest combinatorial structures, configurations are explored from a graphical viewpoint for the first time in this book
- Explores configurations from a graph-theoretical viewpoint
- Includes over two hundred illustrations, challenging exercises at the end of each chapter, a comprehensive bibliography, and a set of open problems
- Well suited for a graduate graph theory course, advanced undergraduate seminar, or self-contained reference for mathematicians and researchers
- Includes supplementary material: sn.pub/extras
Part of the book series: Birkhäuser Advanced Texts Basler Lehrbücher (BAT)
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About this book
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.
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Table of contents (6 chapters)
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Front Matter
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Back Matter
Authors and Affiliations
Bibliographic Information
Book Title: Configurations from a Graphical Viewpoint
Authors: Tomaž Pisanski, Brigitte Servatius
Series Title: Birkhäuser Advanced Texts Basler Lehrbücher
DOI: https://doi.org/10.1007/978-0-8176-8364-1
Publisher: Birkhäuser Boston, MA
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Science+Business Media New York 2013
Hardcover ISBN: 978-0-8176-8363-4Published: 23 September 2012
eBook ISBN: 978-0-8176-8364-1Published: 22 September 2012
Series ISSN: 1019-6242
Series E-ISSN: 2296-4894
Edition Number: 1
Number of Pages: XIII, 279
Number of Illustrations: 229 b/w illustrations, 45 illustrations in colour
Topics: Graph Theory, Geometry, Combinatorics, Topology, Algebraic Geometry