Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come.
The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.
What else is new?
New chapters on measurement and analytic graph theory
Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.
Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth
Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition
Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader
Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.
Table of Contents
INTRODUCTION TO GRAPH MODELS
Graphs and Digraphs
Common Families of Graphs
Graph Modeling Applications
Walks and Distance
Paths, Cycles, and Trees
Vertex and Edge Attributes: More Applications
STRUCTURE AND REPRESENTATION
Graph Isomorphism Revised!
Automorphisms and Symmetry Moved and revised!
Some Graph Operations
Tests for Non-Isomorphism
More Graph Operations
TREES Reorganized and revised!
Characterizations and Properties of Trees
Rooted Trees, Ordered Trees, and Binary Trees
Huffman Trees and Optimal Prefix Codes
Counting Labeled Trees: Prüfer Encoding
Counting Binary Trees: Catalan Recursion
SPANNING TREES Reorganized and revised!
Depth-First and Breadth-First Search
Minimum Spanning Trees and Shortest Paths
Applications of Depth-First Search
Cycles, Edge Cuts, and Spanning Trees
Graphs and Vector Spaces
Matroids and the Greedy Algorithm
Vertex- and Edge-Connectivity
Constructing Reliable Networks
Max-Min Duality and Menger's Theorems
OPTIMAL GRAPH TRAVERSALS
Eulerian Trails and Tours
DeBruijn Sequences and Postman Problems
Hamiltonian Paths and Cycles
Gray Codes and Traveling Salesman Problems
PLANARITY AND KURATOWSKI'S THEOREM Reorganized and revised!
Planar Drawings and Some Basic Surfaces
Subdivision and Homeomorphism
Extending Planar Drawings
Algebraic Tests for Planarity
Crossing Numbers and Thickness
DRAWING GRAPHS AND MAPS Reorganized and revised!
The Topology of Low Dimensions
Mathematical Model for Drawing Graphs
Regular Maps on a Sphere
Imbeddings on Higher-Order Surfaces
Geometric Drawings of Graphs New!
MEASUREMENT AND MAPPINGS New Chapter!
Distance in Graphs New!
Domination in Graphs New!
Intersection Graphs New!
Linear Graph Mappings Moved and revised!
Modeling Network Emulation Moved and revised!
ANALYTIC GRAPH THEORY New Chapter!
Ramsey Graph Theory New!
Extremal Graph Theory New!
Random Graphs New!
SPECIAL DIGRAPH MODELS Reorganized and revised!
Directed Paths and Mutual Reachability
Digraphs as Models for Relations
Project Scheduling and Critical Paths
Finding the Strong Components of a Digraph
NETWORK FLOWS AND APPLICATIONS
Flows and Cuts in Networks
Solving the Maximum-Flow Problem
Flows and Connectivity
Matchings, Transversals, and Vertex Covers
GRAPHICAL ENUMERATION Reorganized and revised!
Automorphisms of Simple Graphs
Graph Colorings and Symmetry
Cycle-Index Polynomial of a Permutation Group
More Counting, Including Simple Graphs
ALGEBRAIC SPECIFICATION OF GRAPHS
Cayley Graphs and Regular Voltages
Symmetric Graphs and Parallel Architectures
NON-PLANAR LAYOUTS Reorganized and revised!
Representing Imbeddings by Rotations
Genus Distribution of a Graph
Voltage-Graph Specification of Graph Layouts
Non KVL Imbedded Voltage Graphs
Heawood Map-Coloring Problem
Relations and Functions
Some Basic Combinatorics
SOLUTIONS AND HINTS New!
Index of Applications
Index of Algorithms
Index of Notations
"This is a huge book, almost 200 pages longer than the already massive first edition. One is tempted to call it, "Everything You Wanted to Know about Graph Theory but Were Afraid to Ask." Nonetheless, Graph Theory and Its Applications is a very good textbook.
What makes it good is strong rapport with the reader, a coherent organization, and consistently clear exposition. The book is aimed at a diverse set of readers. Courses based on this book could be directed toward computer science (concentrating on data structures and algorithms), operation research (focusing on discrete optimization), or mathematics (emphasizing the algebraic and topological aspects). The text is most appropriate for advanced undergraduates or beginning graduate students. Since it is essentially self-contained, it could also be profitably for self-study.
Notable attractive features of the text are breakout boxes with pseudo-code for all significant algorithms (as well as suggestions for specific software implementation), hundreds of examples of graphs carefully integrated with the text, a glossary of terms with each chapter (especially useful in this terminology-heavy field), and a ton of exercises - many with solutions or hints."
- William Satzer, 3M Company
"… an excellent vehicle for either a class text or a self-study reference. The writing is clear … highly recommended … most suitable for an advanced undergraduate in either engineering or computer science."
-Journal of Mathematical Psychology
"I will recommend this book as a text for the next time we teach our graph theory course … this is a well- written book. The authors have done a good job."
- -Computing Reviews
"This book gives an excellent exposition of graphs, graph algorithms and their applications. It builds the theory from the very basics, so it is easy to understand for people not yet skilled in discrete mathematics, but at the same time it gives deep insight into the topics discussed, which is a virtue rarely seen in books on applications."
– In EMS Newsletter, September 2007