Graphs and Digraphs

Graphs and Digraphs

4.06 (15 ratings by Goodreads)
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Description

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theory that have emerged in recent years.The authors have added discussions on topics of increasing interest, deleted outdated material, and judiciously augmented the exercises sections to cover a range of problems that reach beyond the construction of proofs.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; solutions manual covering many of the exercises available to instructors with qualifying course adoptions; and, 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.show more

Product details

  • Hardback | 386 pages
  • 165 x 240 x 30mm | 698.54g
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • United States
  • English
  • Revised
  • 4th Revised edition
  • 163 black & white illustrations
  • 1584883901
  • 9781584883906

Review quote

"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 MATHshow more

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 Referencesshow more

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15 ratings
4.06 out of 5 stars
5 53% (8)
4 27% (4)
3 0% (0)
2 13% (2)
1 7% (1)
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