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Configurations from a Graphical Viewpoint (Hardcover, 2013 ed.)
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Configurations from a Graphical Viewpoint (Hardcover, 2013 ed.)
Series: Birkhauser Advanced Texts / Basler Lehrbucher
Expected to ship within 12 - 17 working days
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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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