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Clear, comprehensive introduction emphasizes graph imbedding but also covers thoroughly the connections between topological graph theory and other areas of mathematics. Discussion of imbeddings into surfaces is combined with a complete proof of the classification of closed surfaces. Authors explore the role of voltage graphs in the derivation of genus formulas, explain the Ringel-Youngs theorem — a proof that revolutionized the field of graph theory — and examine the genus of a group, including imbeddings of Cayley graphs. 1987 edition. Many figures.
- Sales Rank: #810184 in Books
- Published on: 2012-07-17
- Released on: 2012-06-19
- Original language: English
- Number of items: 1
- Dimensions: 8.44" h x .74" w x 5.38" l, .85 pounds
- Binding: Paperback
- 384 pages
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.
About the Author
Jonathan L. Gross is Professor of Computer Science at Columbia University. His research in topology, graph theory, and cultural sociometry has resulted in�a variety of�fellowships and research grants. Thomas W. Tucker is�Mathematics Professor at Colgate University. His research interests include topology, group theory, and�combinatorics.
Most helpful customer reviews
0 of 0 people found the following review helpful.
Some signs of age, and poorly printed (3.0 to 3.5 stars)
By A. J. Sutter
This review is based on using this book as a reference, not on reading it all the way through. One of the strengths of the book is its discussion of the classification of surfaces. It also has a great deal about "voltage graphs," a/k/a gain graphs, a topic that apparently was hot in the 1970s and 1980s, but that you won't find mentioned in modern textbooks like Diestel, Bollab�s or Bondy. (While the two latter books have short sections on electrical networks as an example, a voltage graph was a much broader concept.) As of the end of August 2015, I found only 25 papers on the arXiv that mention voltage or gain graphs in their abstracts, spread over a more than 10-year period.
That's not the only indication that the vocabulary and research areas about graphs on surfaces have come a long way since this book's publication date in 1987 -- in particular, you won't find anything about such current areas of interest as the application of graph theory to knots and links, nor anything about Tutte, Penrose, etc. polynomials, even though these ideas had already been published prior to the book's appearance.
The lack of answers or hints to exercises is definitely a drawback to self-study, despite what another reviewer has proposed. The book has both a "References" list and a "Bibliography," though the difference between them isn't clearly spelled out. (The Dover edition has a supplemental bibliography from around 2001.) There is a subject index only - no name index, so, e.g., you won't be able to find references to Tutte or anyone else very easily.
What really moved me to write this review was the deterioration in Dover's printing. I've been getting their books since the 1960s, and although the books stopped being bound with thread in the 1980s or so, this year (2015) I've gotten a couple of Dovers that really shocked me. This is one of them. The print is fuzzy and unpleasant to read, the paper has a lot of show-through, the product feels bulky: it looks like your usual lousy academic press digital transfer job. And the book doesn't even describe itself as being printed: it was "**Manufactured** in the United States by Courier Corporation." I've bought plenty of Dovers since 2000, when Courier acquired Dover (before being itself acquired by R.R. Donnelly this year); but either it's only recently that they shifted to lower printing quality, or else I had a long string of luck in getting earlier-printed shelf stock. The copy of Gross & Tucker I got was printed in 2013, and another title I got that was even worse than this was from 2015. Prices are jumping up, too, though this particular title is still reasonable as I write. It's worrying to think that Dovers could soon be bad value, thanks to corporate "efficiency," i.e. greed.
10 of 15 people found the following review helpful.
Excellent
By David
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.
3 of 5 people found the following review helpful.
A recognized Classical text
By Roger Bagula
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.
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