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It has become a well-known fact that most graph polynomials are related to the Tutte Polynomial in some way. In fact, that area of graph polynomials has grown to such an extent that it now has its own subject classification (05C31). This handbook is the first one published on the Tutte Polynomial which is a central, heavily-studied object in the field of combinatorics with applications in a wide range of other fields such as geometry, biology and physics.

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...