The study of domination number in Cartesian products has received its main motivation from attempts to settle a conjecture made by V.G Vizing in 1968, where he conjectured that for any two graphs G and H, the product of the domination number of G and the domination number of H is a lower bound for the domination number of the Cartesian product of G and H. Most of the progress in settling this conjecture has been limited to verifying the conjectured lower bound if one of the graphs has some structural property. However, several authors have established various bounds for dominating the Cartesian product of any two graphs. It is the purpose of this book to present a comprehensive study on Vizing's conjecture. Hopefully, this paves the way for the long-awaited proof for this outstanding conjecture. On the other hand, this book settles some previously open problems concerning the case when the conjectured bound is sharp. Some open problems, as well as a conjecture related to Vizing's conjecture, are presented.
Product Identifiers
Publisher
LAP
ISBN-13
9783659645358
eBay Product ID (ePID)
213297611
Product Key Features
Author
Nazzal Khalida M
Publication Name
On the Domination Number of the Cartesian Product of Graphs