Reverse Signed Domination Of Graph

As an important research field in graph theory, domination theory has many and varied applications in related science fields, such as combinatorial optimization,computer science, communication network, sociology and so on. In recent years, the form and the definition of domination theory is more and more diversified. At the same time, because of domination theory is NP-complete problems, the upper and lower bounds of domination numbers as well as their relationship is the main aspect of recent research. This thesis mainly study three domination numbers:reverse signed edge domination, reverse signed edge total domination and reverse signed edge total k domination. It mainly includes the following three parts:(1) We give two new upper bounds of of reverse signed edge domination numbers of general graphs and a upper bound of regular connected graphs only depends on its points.(2) We give a inference and two new upper bounds of of reverse signed edge total domination numbers of general graphs.(3) We new define a class of domination-reverse signed edge total k domination. We also give two upper bounds of of reverse signed edge total k domination numbers of general graphs.