Topics in Graph Theory

This book presents the basic facts about the Cartesian product, and relates them to Hamming graphs and Tower of Hanoi graphs. It focuses on the domination number of a graph with special emphasis on the famous conjecture of Vizing and several different graph coloring invariants.

From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way, this book can be used for personal study in advanced applications of graph theory or for an advanced graph theory course.

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

Inhalt
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