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

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


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About the Book

With a growing range of applications in fields from computer science to chemistry and communications networks, graph theory has enjoyed a rapid increase of interest and widespread recognition as an important area of mathematics. Through more than 20 years of publication, Graphs & Digraphs has remained a popular point of entry to the field, and through its various editions, has evolved with the field from a purely mathematical treatment to one that also addresses the mathematical needs of computer scientists. Carefully updated, streamlined, and enhanced with new features, Graphs & Digraphs, Fourth Edition reflects many of the developments in graph theory that have emerged in recent years. The authors have added discussions on topics of increasing interest, deleted outdated material, and judiciously augmented the Exercises sections to cover a range of problems that reach beyond the construction of proofs. New in the Fourth Edition: Expanded treatment of Ramsey theory Major revisions to the material on domination and distance New material on list colorings that includes interesting recent results A solutions manual covering many of the exercises available to instructors with qualifying course adoptions A comprehensive bibliography including an updated list of graph theory books Every edition of Graphs & Digraphs has been unique in its reflection the subject as one that is important, intriguing, and most of all beautiful. The fourth edition continues that tradition, offering a comprehensive, tightly integrated, and up-to-date introduction that imparts an appreciation as well as a solid understanding of the material.

Table of Contents:
INTRODUCTION TO GRAPHS AND DIGRAPHS
Graphs
Degree Sequences
Connected Graphs and Distance
Digraphs and Multigraphs
THE STRUCTURE OF GRAPHS
Cut-Vertices, Bridges and Blocks
The Automorphism Group of a Graph
Cayley Color Graphs
The Reconstruction Problem
TREES AND CONNECTIVITY
Elementary Properties of Trees
Arboricity and Vertex-Arboricity
Connectivity and Edge-Connectivity
Menger's Theorem
The Toughness of a Graph
EULERIAN AND HAMILTONIAN GRAPHS AND DIGRAPHS
Eulerian Graphs and Digraphs
Hamiltonian Graphs and Digraphs
Line Graphs and Powers of Graphs
DIRECTED GRAPHS
Strong Digraphs
Tournaments
Hamiltonian Tournaments
PLANAR GRAPHS
The Euler Identity
Characterizations of Planar Graphs
Hamiltonian Planar Graphs
Crossing Number and Thickness
GRAPH EMBEDDINGS
The Genus of a Graph
2-Cell Embeddings of Graphs
The Maximum Genus of a Graph
GRAPH COLORINGS
Vertex Colorings
Edge Colorings
Map Colorings and Flows
MATCHINGS, FACTORS AND DECOMPOSITIONS
Matchings and Independence in Graphs
Factorizations and Decompositions
Labelings of Graphs
DOMINATION IN GRAPHS
The Domination Number of a Graph
The Independent Domination Number of a Graph
Other Domination Parameters
EXTREMAL GRAPH THEORY
Tura'n's Theorem
Extremal Results on Graphs
Cages
RAMSEY THEORY
Classical Ramsey Numbers
Generalized Ramsey Theory
Rainbow Ramsey Numbers
THE PROBABILISTIC METHOD IN GRAPH THEORY
The Probabilistic Method
Random Graphs

Glossary of Symbols
Graph Theory Books
References

Review :
"a popular point of entry to the fieldhas evolved with the field from a purely mathematical treatment to one that also addresses the needs of computer scientists." -L'Enseignement Mathimatique "emphasizes clear exposition, well-written proofs, and many original and innovative exercises-of varying difficulty and challengeFor 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: 9781584883906
  • Publisher: Taylor & Francis Ltd
  • Publisher Imprint: Chapman & Hall/CRC
  • Edition: New edition
  • Language: English
  • No of Pages: 386
  • Series Title: Textbooks in Mathematics
  • Width: 156 mm
  • ISBN-10: 1584883901
  • Publisher Date: 28 Oct 2004
  • Binding: Hardback
  • Height: 235 mm
  • No of Pages: 386
  • Returnable: N
  • Weight: 703 gr


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