Ellis-Monaghan J.A., Moffatt I. Graphs on Surfaces: Dualities, Polynomials, and Knots

Springer, 2013. — 149 p. — (SpringerBriefs in Mathematics). — ISBN: 978-1-4614-6970-4.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.Embedded Graphs
Generalised Dualities
Twisted Duality, Cycle Family Graphs, and Embedded Graph Equivalence
Interactions with Graph Polynomials
Applications to Knot Theory