Graph Theory and Its Applications, Second Edition
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.
- Hardback | 800 pages
- 175.3 x 256.5 x 48.3mm | 1,383.47g
- 23 Sep 2005
- Taylor & Francis Ltd
- Chapman & Hall/CRC
- Boca Raton, FL, United States
- New edition
- 2nd New edition
- 4 Tables, black and white; 582 Illustrations, black and white
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Table of contents
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: Prufer 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