The Fascinating World of Graph Theory

by Arthur T. Benjamin, Gary Chartrand, Ping Zhang

Graph theory goes back several centuries and revolves around the study of graphs―mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics―and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

Genres: Mathematics, Nonfiction, Science

344 pages, Hardcover

First published December 24, 2014

About the author

Arthur Benjamin holds a PhD from Johns Hopkins University and is a professor of mathematics at Harvey Mudd College, where he has taught since 1989. He is a noted “mathemagician,” known for being able to perform complicated computations in his head. He is the author, most recently, of The Secrets of Mental Math, and has appeared on The Today Show and The Colbert Report. Benjamin has been profiled in such publications as the New York Times, the Los Angeles Times, USA Today, Scientific American, Discover, and Wired.

Reviews

[Jack Duncan · Rating 3 out of 5]

My classmates hate this book because every chapter starts with a long winded history lesson on the idea behind each chapter. It’s really unnecessary and just wasted a lot of time. I loved this book because every chapter starts with a long winded history lesson on the idea behind each chapter. It’s really unnecessary and just wasted a lot of time.

[Alexander Telfar · Rating 2 out of 5]

After being spoilt by 3Blue1Brown/ViHart/Numberphile, this book doesnt live up to the great standard I am used to.

Half the time I found myself looking up definitions in Wikipedia because the book's definitions were a little too concise...

While the pictures are nice, I found that the authors did little to make the proofs more easily understandable. Rather they were a mixture of natural and formal language. I would have preferred totally formal and well organised proofs, paired with some intuition and explanation via language/visuals.

I struggled to get through this book, I struggled to care. There were few real world examples (at least not enough for me).
For example, to sample a random topic; some regular graphs can be factored into subgraphs. Cool... Maybe I would be more interested if the idea was quite general (you showed me that the factorization can be used as a basis for describing arbitrary graphs), or that there is a real world use, or that the theorems could be connected to other types of math (abstract algebra and symmetry, eigen analysis, ...).

Also, there was a decent focus on the mathematicians of group theory, giving some of their history and biographies. Neither good nor bad.

I guess I am still yet to be inspired and excited by graph theory, at least as presented in this book. To be fair, I didnt really engage much with the book, the exercises etc.

[Tim Gautier · Rating 3 out of 5]

I really would have like some more practical applications of graph theory. There were a few, but just not enough and it really goes off into the theoretical weeds often.

[Clouds Lee · Rating 5 out of 5]

Hard-core mathematical theories mixed with historical anecdotes, insightful and delightful.

[danielle; ▵ · Rating 4 out of 5]

but I mean, how fascinating is a world where just four colors are sufficient to color any map, really?

[Charles · Rating 4 out of 5]

Graph theory is one of the easiest areas to intuitively understand, it is fundamentally a set of positions and connections between them. The simplest and yet best comment I ever heard was when one of the students in my class said, “It is like modeling moves in checkers.” When I was teaching discrete mathematics, it was one of the areas that the students had the easiest time with. While this book contains some of the advanced problems in graph theory and includes theorems with proofs, it is a book that is still close to where it could be described as popular mathematics.
The main point that people unfamiliar with graph theory will find surprising is the breadth of areas where it can be applied. Using many of the classic problems of graph theory such as the bridges of Konigsberg, knight’s tours and the Four Color Problem, the power of graph theory to reduce a problem down to the essence is demonstrated.
It is also a history of graph theory; many of the people that made the greatest contributions are briefly profiled. As I was reading this book my thought was that this would be an excellent text for courses in graph theory for non math majors where there is to be some significant content. Given the widespread use of graphs in the analysis of complex project analysis, PERT and computer networking charts come to mind, this is a book that will give the history and some theory regarding how graphs are used.
I have taught computer networking and management science classes and graph theory is used in both courses. Plotting efficient delivery or transit routes is an important part of how business is done in the modern world and an understanding of graph theory as presented in this book is essential if you are to understand how to do it.

This book was made available for free for review purposes and this review appears on Amazon.

[Hypatia · Rating 3 out of 5]

This was a little more mathematical than I was expecting when I picked it up. I found it interesting, but really had to pay attention to follow some of the explanations and psuedo-proofs. I also thought the writing was not very good in places. It seemed stilted and abrupt, with chapters either ending suddenly (more than once I found myself double checking to see if I'd skipped a page) or ending with some tacked-on sentences about the subsequent career of some mathematician. Overall, interesting, but not a great read. The authors state in their introduction that this could be used as a textbook, and I think it does lean more that way than a good popularization of graph theory.

[Lloyd Fassett]

1/31/14 found it browsing in science section at Powell's in Portland