Topological Graph Theory (Dover Books on Mathematics) [Paperback]

Jonathan L. Gross (Author), Thomas W. Tucker (Author), Mathematics (Author)

Book Description

Publication Date: August 16, 2012 | Series: Dover Books on Mathematics

Iintroductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem, and examine the genus of a group, including imbeddings of Cayley graphs. Many figures. 1987 edition.

Editorial Reviews

From the Publisher

This definitive treatment written by well-known experts emphasizes graph imbedding while providing thorough coverage of the connections between topological graph theory and other areas of mathematics: spaces, finite groups, combinatorial algorithms, graphical enumeration, and block design. Almost every result of studies in this field is covered, including most proofs and methods. Its numerous examples and clear presentation simplify conceptually difficult material, making the text accessible to students as well as researchers. Includes an extensive list of references to current literature. --This text refers to an out of print or unavailable edition of this title.

Product Details

• Paperback: 384 pages
• Publisher: Dover Publications (August 16, 2012)
• Language: English
• ISBN-10: 0486417417
• ISBN-13: 978-0486417417
• Product Dimensions: 8.4 x 5.4 x 0.7 inches
• Shipping Weight: 8 ounces
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,836,076 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

3 of 3 people found the following review helpful:

4.0 out of 5 stars A recognized Classical text, December 8, 2006

By 

R. Bagula "Roger L. Bagula" (Lakeside, Ca United States) - See all my reviews
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This review is from: Topological Graph Theory (Dover Books on Mathematics) (Paperback)

This book had much that I needed to know about graph theory.

It is well written and includes much of the information needed.

It has three problems in notation that bother me:

1) Bn for Bouquets is like the Bn used for Braid groups.

2) definitions of "stars" are more the classical star than

the current usage as central point with radial connections.

3)The book doesn't distinguish well enough

between "graphs" with are symmetrical adjacency matrices

and "digraphs" and ends up confusing the issue it should clarify.

The book also shorts the reader on matrix theory connected to the graphs.

It tends to use an older approach to graphs that has to be adapted to modern computer mathematical systems.

9 of 12 people found the following review helpful:

4.0 out of 5 stars Excellent, January 4, 2004

By 

David Diez (Boston, MA) - See all my reviews

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This review is from: Topological Graph Theory (Dover Books on Mathematics) (Paperback)

This book is written at a graduate level. It is written, for the most part, clearly and methodically. There are about 300 problems throughout the text, but there are no solutions in this book for those problems.

Titles of the 6 Chapters (with the number of pages in each chapter): 1) Introduction (to graph theory), 55; 2) Voltage Graphs and Covering Spaces, 40; 3) Surfaces and Graph Embeddings, 68; 4) Imbedded Voltage Graphs and Current Graphs, 54; 5) Map Colorings, 35; and 6) The Genus of a Group, 71.

This book is sufficient for self-study.