Graph Theory and Its Applications

Rating:
Summary: Plain and simple: EXCELLENT book
Review:
This is a superb book for an introduction to graph theory. It is not just a pile of theorems as other books you'll find in this field. It presents insight and intuition first, and then it gives the necessary formal treatment. The topics covered are perfect, in the right order. Extremelly recommended for anyone eagerly wanting a first contact with this exciting field, as well as for any graph theory instructor looking for the right book to follow in class.

Rating:
Summary: Graph Theory and Its Applications
Review: Graph Theory and Its Applications is a comprehensiveapplications-driven Upper division/first year graduate level textbookthat provides material for several different courses in graph theory.

First author, Gross, is an experienced textbook author. MS material currently being class-tested at Columbia University & Florida Institute of Technology.

Topics Include:

* Trees, connectivity, planarity, coloring;

* Graphical models for electrical and communications networks and computer architectures;

* Network optimization models for operations analysis, including scheduling and job assignment;

* Voltage graphs, algebraic specification of graphs (including the wrapped butterfly), and other topics that showcase the interplay between graph theory and algebra.

Features:

* Applications and concrete examples -- help demonstrate relevance;

* More than 700 graph drawings -- promote spatial intuition;

* More than 1,600 exercises -- from routine practice to more challenging problem solving;

* Algorithms -- in a concise, easy-to-read format

Rating:
Summary: A great link between math and computer sciences
Review: Professors Gross and Yallen have written a great book on "practical" graph theory that can be used in math or computer sciences courses alike. The book is very well organized and its chapters can be read on almost any sequence, allowing instructors to skip sections or give special emphasis to certain more interesting subjects.

The text can be used in a one semester introductory graduate course in graph theory in a CS or math department, an advanced undergraduate seminar or as a reference book for an undergraduate course in discrete math.

Of special interest are the sections on Huffman trees and voltage graphs. The section on Hoffman trees is especially interesting to computer scientists. I believe this is the first book that devotes an entire section to the theoretical treatment of this very useful subject. Prof. Gross is a pioneer in voltage graphs and the treatment of this somewhat esoteric subject is lucid and complete.

Overall this textbook is excellent. The writing is clear and precise and the knowledge needed to read it is that of an advanced undergraduate student. However, the book could benefit from solutions to the exercises, or at least some selected exercises, some computer sciences oriented "practical" examples and projects and an instructor's manual.

Rating:
Summary: A great link between math and computer sciences
Review: Professors Gross and Yallen have written a great book on "practical" graph theory that can be used in math or computer sciences courses alike. The book is very well organized and its chapters can be read on almost any sequence, allowing instructors to skip sections or give special emphasis to certain more interesting subjects.

The text can be used in a one semester introductory graduate course in graph theory in a CS or math department, an advanced undergraduate seminar or as a reference book for an undergraduate course in discrete math.

Of special interest are the sections on Huffman trees and voltage graphs. The section on Hoffman trees is especially interesting to computer scientists. I believe this is the first book that devotes an entire section to the theoretical treatment of this very useful subject. Prof. Gross is a pioneer in voltage graphs and the treatment of this somewhat esoteric subject is lucid and complete.

Overall this textbook is excellent. The writing is clear and precise and the knowledge needed to read it is that of an advanced undergraduate student. However, the book could benefit from solutions to the exercises, or at least some selected exercises, some computer sciences oriented "practical" examples and projects and an instructor's manual.

Rating:
Summary: great, comprehensive introduction
Review: Regardless of whether you just want to implement a couple of graph algorithms or get into the guts of graph theoretic proofs, this book should come in as a great resource.

In over 500 pages, this book covers a lot of ground beyond the basics, such as topology of graphs, graph operations and mappings, voltage graphs, and surface imbeddings. Definitions are very clear, propositions and proofs are stated very clearly, and there are shrink-wrapped algorithms if you just want to apply them.

Requiring no previous knowledge of abstract algebra or graph theory, this is a great resource to have in your bookshelf.

Rating:
Summary: not recommended
Review: This book was used for my undergraduate course in introductory graph theory, which was split between math and computer science students. I found that this book left to be desired. The definitions are imprecise and often inconsistent with those that are standard, and much of the notation used is not standard. I would not recommend this book as a reference or for advanced students.

Rating:
Summary: A(nother) wonderful graph theory book!
Review: This recently published book in graph theory has many unique features: (1) it contains a large number of figures that make it much easier to follow and understand the mathematical reasonnings; (2) it contains a lot more recent developments in the area that are not covered in general graph theory books; (3) it shows close connections of this area to other areas, in particular to computer science, which greatly increase the usefulness of the book; (4) the book is so well written that can be understood by people with very preliminary knowledge in mathematics (most parts can be understood by people with, say, high school mathematics).

I really like the book, and I recommend it very highly.