Topics in Graph Theory

Imrich, Wilfried; Klavzar, Sandi; Rall, Douglas F

" more to graphs than the average person would ever know. Topics in Graph Theory: Graphs and Their Cartesian Product is a scholarly textbook of graph theory; a quarter of the book is dedicated to exercises and their complete solutions. Chapters cover Cartesian products, more classical products such as Hamiltonian graphs, invariants, algebra and other topics. Topics in Graph Theory: Graphs and Their Cartesian Product is an ideal text for classroom or self-study. " -Library Bookwatch, April 2009 "This excellent textbook addresses a reader who wishes to apply graph theory at a higher or more special level. The prerequisites are previous exposure to fundamental notions of graph theory, discrete mathematics, and algebra." -Zentralblatt MATH, March 2009 "This book is focused on the Cartesian product of graphs. This graph operation stems from algebraic and categorical concepts and the prime and simplest example is the hypercube - the Cartesian power of a single edge. With the wealth of well-known results on hypercubes ... , it is worthwhile to explore the realm of products of graphs. Many classical topics are discussed with respect to the Cartesian product. ... The book is suitable for advanced undergraduates or beginning graduate students interested in graph theory." -Newsletter of the European Mathematical Society , September 2009 "All three authors being among the leading researchers in the area of graph products, it is not surprising that the new book contains many state-of-the art results which appeared at about the same time as this book. Even before its release the book was thoroughly tested in several graduate-level course's at the authors' home universities. ... An especially valuable part of the book are the more than 200 exercises which conclude every chapter. ... Researchers in graph theory will find in this book an encyclopedia of known results on graph products, and teachers will welcome it as an excellent textbook. It will also be enjoyed by all other devotees of graph theory wishing to learn the state of the art in this area." -Marko Petkovsek, Obzornik Mat. Fiz., December 2009 "The format and style is ideally suited to an honours or post-graduate seminar series... [The book] would be a useful addition to any university library." -Lakoa Fitina, Australian Mathematical Society, March 2010"

• Part I: Cartesian Products 1. The Cartesian Product 2. Hamming Graphs and Hanoi Graphs Part II: Classic Topics 3. Hamiltonian Graphs 4. Planarity and Crossing Number 5. Connectivity 6. Subgraphs Part III: Graphical Invariants 7. Independence 8. Graph Colorings 9. Additional Types of Colorings 10. Domination 11. Domination in Cartesian Products Part IV: Metric Aspects 12. Distance Lemma and Wiener Index 13. Products and Boxes 14. Canonical Metric Representation Part V: Algebraic and Algorithmic Issues 15. Prime Factorizations 16. Cancelation and Containment 17. Distinguishing Number 18. Recognition Algorithms