Topics in Graph Theory

The interplay between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences continues to grow.

The interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences.

Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level.

The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material.

** Features

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• Extensive exercises and applications.

• Flexibility: appropriate for either a first course at the graduate level or an advanced course at the undergraduate level.

• Opens avenues to a variety of research areas in graph theory.

• Emphasis on topological and algebraic graph theory.

  Autorentext

Mark Anderson is a professor of mathematics and computer science at Rollins College. His research interests in graph theory center on the topological or algebraic side. ** Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. ** Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms.

Inhalt

1. Foundations. 2. Isomorphisms and Symmetry. 3. Trees and Connectivity. 4. Planarity and Kuratowski's Theorem. 5. Drawing Graphs and Maps. 6. Graph Colorings. 7. Measurement and Mappings. 8. Analytic Graph Theory. 9. Graph Colorings and Symmetry. 10. Algebraic Specification of Graphs. 11. Nonplanar Layouts.