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Home > Mathematics and Science books > Mathematics > Combinatorics and graph theory > Graphs & Digraphs, Fifth Edition: (Textbooks in Mathematics)
Graphs & Digraphs, Fifth Edition: (Textbooks in Mathematics)

Graphs & Digraphs, Fifth Edition: (Textbooks in Mathematics)


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About the Book

Continuing to provide a carefully written, thorough introduction, Graphs & Digraphs, Fifth Edition expertly describes the concepts, theorems, history, and applications of graph theory. Nearly 50 percent longer than its bestselling predecessor, this edition reorganizes the material and presents many new topics. New to the Fifth Edition New or expanded coverage of graph minors, perfect graphs, chromatic polynomials, nowhere-zero flows, flows in networks, degree sequences, toughness, list colorings, and list edge colorings New examples, figures, and applications to illustrate concepts and theorems Expanded historical discussions of well-known mathematicians and problems More than 300 new exercises, along with hints and solutions to odd-numbered exercises at the back of the book Reorganization of sections into subsections to make the material easier to read Bolded definitions of terms, making them easier to locate Despite a field that has evolved over the years, this student-friendly, classroom-tested text remains the consummate introduction to graph theory. It explores the subject's fascinating history and presents a host of interesting problems and diverse applications.

Table of Contents:

Introduction to Graphs
Graphs and Subgraphs
Degree Sequences
Connected Graphs and Distance
Multigraphs and Digraphs

Trees and Connectivity
Nonseparable Graphs
Trees
Spanning Trees
Connectivity and Edge-Connectivity
Menger’s Theorem

Eulerian and Hamiltonian Graphs
Eulerian Graphs
Hamiltonian Graphs
Powers of Graphs and Line Graphs

Digraphs
Strong Digraphs
Tournaments
Flows in Networks

Graphs: History and Symmetry
Some Historical Figures of Graph Theory
The Automorphism Group of a Graph
Cayley Color Graphs
The Reconstruction Problem

Planar Graphs
The Euler Identity
Planarity versus Nonplanarity
The Crossing Number of a Graph
Hamiltonian Planar Graphs

Graph Embeddings
The Genus of a Graph
2-Cell Embeddings of Graphs
The Maximum Genus of a Graph
The Graph Minor Theorem

Vertex Colorings
The Chromatic Number of a Graph
Color-Critical Graphs
Bounds for the Chromatic Number
Perfect Graphs
List Colorings

Map Colorings
The Four Color Problem
Colorings of Planar Graphs
The Conjectures of Hajós and Hadwiger
Chromatic Polynomials
The Heawood Map-Coloring Problem

Matchings, Factorization, and Domination
Matchings and Independence in Graphs
Factorization
Decomposition and Graceful Graphs
Domination

Edge Colorings
Chromatic Index and Vizing’s Theorem
Class One and Class Two Graphs
Tait Colorings
Nowhere-Zero Flows
List Edge Colorings and Total Colorings

Extremal Graph Theory
Turán’s Theorem
Cages
Ramsey Theory

Hints and Solutions to Odd-Numbered Exercises
Bibliography
Index of Names
Index of Mathematical Terms
List of Symbols



About the Author :
Gary Chartrand is a professor emeritus of mathematics at Western Michigan University. Linda Lesniak is a professor emeritus of mathematics at Drew University. Ping Zhang is a professor of mathematics at Western Michigan University. All three have authored or co-authored many textbooks in mathematics and numerous research articles in graph theory.

Review :
Praise for the Fourth Edition ! a popular point of entry to the field ! has evolved with the field from a purely mathematical treatment to one that also addresses the needs of computer scientists. --L'Enseignement Mathematique ! emphasizes clear exposition, well-written proofs, and many original and innovative exercises of varying difficulty and challenge ! For 25 years, Graphs & Digraphs, in its various editions, has served as an exemplary introduction to the emerging mathematical disciplines of graph theories, for advanced undergraduate and graduate students. It has also served established graph theorists, combinatorialists, and other discrete mathematicians, as well as computer scientists and chemists, as a useful reference work. The fourth edition continues these fine traditions. --Zentralblatt MATH


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Product Details
  • ISBN-13: 9781439826270
  • Publisher: Taylor & Francis Inc
  • Publisher Imprint: Taylor & Francis Inc
  • Edition: New edition
  • Language: English
  • No of Pages: 598
  • Series Title: Textbooks in Mathematics
  • Width: 156 mm
  • ISBN-10: 1439826277
  • Publisher Date: 19 Oct 2010
  • Binding: Hardback
  • Height: 234 mm
  • No of Pages: 598
  • Returnable: N
  • Weight: 975 gr


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