Study On Domination Parameters Of Graphs

The domination parameters play an important part in the structure of graphs. With the development of practical problems, the types of domination parameters are increasing. There are many research results in this aspect recently. These results not only promotes the development of graph theory, but also is of great significance in applying graph theory to practice.In this paper, firstly, we introduce several types of domination parameters, we also introduce a constructive characterization of the trees T such that one domination number of T is equal to another, then we study the trees T such that one domination number of T is strong equal to another. Secondly, we study the paired domination number and the double domination number of Petaline Graphs and Adjacency graphs, we show that the paired domination number is less than or equal to the double domination number for Petaline Graphs and Adjacency graphs, and also we characterize the Petaline Graphs and Adjacency graphs with equal paired and double domination numbers. Finally, we introduce and summarize the domination number of product graph, then we discuss the domination number of join graph.