Several Types Of Total Signed Dominations In Graphs

This paper is mainly to the several types of total signed dominations in graphs, focuses on total signed dominations of the three types of problems that total signed domination, reverse total signed domination and total signed local domination.In this paper, from the following aspects:First, we begin by reviewing the basic concept of the graph and signed domination, signed edge domination of the graph of research status and has been derived from some basic conclusions. As the basis for laying the groundwork of the main content of our study.Second, we discuss total signed domination numbers of bounds in graph. Total signed domination in graph by the Lanzhou Railway Institute, Jinbu Lu and Linzhong Liu first introduced in2001, and gives its definition, as well as some special graphs. Xinzhong Lv teacher then be more in-depth study to total signed domination numbers of bounds in theorems. In this paper, we mainly its general graphs gives a better bound, at the same time gives more special graphs (such as star graph, circle graph, road graph, fan graph, wheel graph, complete bipartite graph, etc.) total signed domination number of bounds.Third, we are on total signed domination to promote, I have introduced the reverse total signed domination of graph, and gives its definition and some simple nature, and then we give a general diagram of the reverse total signed domination number of bound and the reverse total signed domination number of some special graphs of bound.At last, we discuss total signed domination were extended, give the definition of total signed local domination of the graph, some improvements in the research of others on the basis of its total signed local number of bound to determine the total signed local number of the star graph and the complete bipartite graph the upper and lower bound.