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Graphs on Surfaces - Dualities, Polynomials, and Knots (Paperback, 2013 ed.)
Loot Price: R1,933
Discovery Miles 19 330
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Graphs on Surfaces - Dualities, Polynomials, and Knots (Paperback, 2013 ed.)
Series: SpringerBriefs in Mathematics
Expected to ship within 12 - 17 working days
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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.
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