Graphs of Groups on Surfaces: Interactions and Models Volume 188 Contributor(s): White, A. T. (Author) |
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ISBN: 0444500758 ISBN-13: 9780444500755 Publisher: North-Holland OUR PRICE: $207.90 Product Type: Hardcover - Other Formats Published: April 2001 Annotation: 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 church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings.
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Additional Information |
BISAC Categories: - Mathematics | Graphic Methods - Mathematics | Discrete Mathematics - Mathematics | Group Theory |
Dewey: 511.5 |
LCCN: 2001030789 |
Series: North-Holland Mathematics Studies |
Physical Information: 0.81" H x 6.66" W x 9.68" (1.85 lbs) 378 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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 church-bell music. The latter is facilitated by imbedding the right graph of the right group on an appropriate surface, with suitable symmetries. Throughout the emphasis is on Cayley maps: imbeddings of Cayley graphs for finite groups as (possibly branched) covering projections of surface imbeddings of loop graphs with one vertex. This is not as restrictive as it might sound; many developments in topological graph theory involve such imbeddings.
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