Graph Theory and Its Applications (Textbooks in Mathematics)

Gross, Jonathan L.; Yellen, Jay

ISBN 10: 158488505X / ISBN 13: 9781584885054

Editore: Chapman and Hall/CRC, 2005

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Dati bibliografici

• Titolo: Graph Theory and Its Applications (Textbooks in Mathematics)
• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 158488505X
• ISBN 13: 9781584885054
• Rilegatura: Rilegato
• Edizione: seconda edizione
• Condizione: acceptable

Descrizione articolo

Riassunto

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.

Contenuti

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