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The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
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The book, suitable as both an introductory reference and as a text book in the rapidly growing field of topological graph theory, models both maps (as in map-coloring problems) and groups by means of graph imbeddings on sufaces. Automorphism groups of both graphs and maps are studied. In addition connections are made to other areas of mathematics, such as hypergraphs, block designs, finite geometries, and finite fields. There are chapters on the emerging subfields of enumerative topological graph theory and random topological graph theory, as well as a chapter on the composition of English
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Topology --- Discrete mathematics --- Topological graph theory. --- Graphes topologiques, Théorie des. --- Topological graph theory --- Graph theory
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Discrete mathematics --- Topological graph theory --- Knot theory --- Link theory --- Low-dimensional topology --- Piecewise linear topology --- Knots (Topology) --- Graph theory --- Topology --- Topological graph theory. --- Graphes topologiques, Théorie des. --- Knot theory. --- Noeuds, Théorie des. --- Link theory. --- Lien, Théorie du.
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