Research On The Total Signed Domination Number Of Some Graph Classes

Signed domination is an important research direction of graph theory, not only in real life has a very wide range of applications, for example, the launch of the base station location, computer communication network and group decision making and so on, and it’s on the optimization theory, computational complexity and algorithm design, communication network design and analysis, etc have also been widely used. Studying NP-hard problem can help us to get the important reference and solve the problem at last. These studies have been received extensive attention of many scholars.In this paper, we study the total signed domination number of the Cartesian product of a path Pm and a cycle Cn. According to the signed dominating type and the properties of the vertex neighborhood and edge neighborhood in graphs, we can deduce its lower bounds. Let G be a finite connected simple graph with a vertex set V(G) and an edge set E(G). For any G,we can get the following conclusion:Then we use computer to construct upper bound of total signed domination number.The key figure class in computer algorithm is according to the different characteristics of graphs to design an effective branch limit conditions, thus to guide the computer gradually construct appropriate total signed dominating function and use it to give a better signed domination number boundary.At last we can get the final conclusion.