Graphs & Digraphs, Fifth Edition

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Product Description

Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics.

New to the Fifth Edition

• New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings


• New examples, figures, and applications to illustrate concepts and theorems


• Expanded historical discussions of well-known mathematicians and problems


• More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book


• Reorganization of sections into subsections to make the material easier to read


• Bolded definitions of terms, making them easier to locate

Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject s fascinating history and presents a host of interesting problems and diverse applications.

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Graphs & Digraphs, Fifth Edition Review

This book contains a lot of material and covers it very well. The discipline of graph theory is a broad one, and no textbook could possibly cover all of it, but Graphs and Digraphs gets as close to it as you are likely to find in a single book.

The proofs and theorems are stated and proved quickly, giving brief examples only when it feels they are needed. I can see how this would be irritating to a great many students, but this choice allows it to cover far more material without spending pages getting bogged down in extraneous fluff.

The end-of-section questions are extremely well thought out. Where many textbooks only ask students to repeat back to the instructor what they read this one expects the students to think before coming up with an answer. The authors assume that the reader wants to master the subject and therefore needs to learn how to think like a graph theorist and so they ask questions that make the reader work for an answer. I personally prefer this philosophy of textbook writing.

I feel the need to offer a caveat. This book is for those that want to learn graph theory as opposed to those that want to use graph theory. If you are a computer scientist or someone else that wants a reference that will help with writing and analyzing algorithms I would skip over this book unless you are willing to spend the time and effort to learn the subject inside and out, including those parts of graph theory that have no relevance to whatever it is you are working on. The book is very unforgiving toward those that skip past the part where new vocabulary and concepts are introduced.

Chapter Titles:
1. Introduction to Graphs
2. Trees and Connectivity
3. Eulerian and Hamiltonian Graphs
4. Digraphs
5. Graphs: History and Symmetry
6. Planer Graphs
7. Graph Embeddings
8. Vertex Colorings
9. Map Colorings
10. Matchings, Factorization and Domination
11. Edge Colorings
12. Extremal Graph Theory

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