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!
Subgraphs
Some Graph Operations
Tests for Non-Isomorphism
Matrix Representation
More Graph Operations

TREES Reorganized and revised!
Characterizations and Properties of Trees
Rooted Trees, Ordered Trees, and Binary Trees
Binary-Tree Traversals
Binary-Search Trees
Huffman Trees and Optimal Prefix Codes
Priority Trees
Counting Labeled Trees: Prüfer Encoding
Counting Binary Trees: Catalan Recursion

SPANNING TREES Reorganized and revised!
Tree-Growing
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

CONNECTIVITY Revised!
Vertex- and Edge-Connectivity
Constructing Reliable Networks
Max-Min Duality and Menger's Theorems
Block Decompositions

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
Kuratowski's Theorem
Algebraic Tests for Planarity
Planarity Algorithm
Crossing Numbers and Thickness

DRAWING GRAPHS AND MAPS Reorganized and revised!
The Topology of Low Dimensions
Higher-Order Surfaces
Mathematical Model for Drawing Graphs
Regular Maps on a Sphere
Imbeddings on Higher-Order Surfaces
Geometric Drawings of Graphs New!

GRAPH COLORINGS
Vertex-Colorings
Map-Colorings
Edge-Colorings
Factorization New!

MEASUREMENT AND MAPPINGS New Chapter!
Distance in Graphs New!
Domination in Graphs New!
Bandwidth 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
Tournaments
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
Burnside's Lemma
Cycle-Index Polynomial of a Permutation Group
More Counting, Including Simple Graphs
Polya-Burnside Enumeration

ALGEBRAIC SPECIFICATION OF GRAPHS
Cyclic Voltages
Cayley Graphs and Regular Voltages
Permutation Voltages
Symmetric Graphs and Parallel Architectures
Interconnection-Network Performance

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

APPENDIX
Logic Fundamentals
Relations and Functions
Some Basic Combinatorics
Algebraic Structures
Algorithmic Complexity
Supplementary Reading

BIBLIOGRAPHY
General Reading
References

SOLUTIONS AND HINTS New!

INDEXES
Index of Applications
Index of Algorithms
Index of Notations
General Index

Reviews

"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