Signed Edge Total Domination Number Of Graphs

In recent decades, as an important part of applied mathematics, Graph Theory has in rapid development. As important parameters of graph, domination-related pa-rameters have close connection with combinational optimization-, theoretical computer science、communications in networks、sociology and other fields. Thus the research of domination-related parameters have important significance. The research of the con-cepts and results of domination-related parameters are almost always about the points of graph, such as domination、signed domination、major domination、k signed dom-ination、domatic domination、minus domination、inverse domination, but it is rarely involved the problems of edges. In the last two decades, signed edge domination has been widespread concerned. In order to enrich and improve signed edge domination theory, this paper studies signed edge total domination number of graphs and signed domination about k.This master thesis consists of three chapters.In Chapter 1, we collect some basic notations, give a chief survey in this direction and state the main results obtained.In Chapter 2, we study the signed total edge domination number of graphs with the following two sections:(1) The lower bound of the signed edge total domination number for cubic graphs.(2) The lower bound of the signed edge total domination number for complete bi-partite graphs.In Chapter 3, we define and study the signed edge domination number related to k with the following two sections:(1) The upper bound of the signed edge domination number for 3-regular bipartite graphs, and the lower bound of the signed edge domination number for connected graphs.(2) The signed edge distance k domination number for 3-regular bipartite graphs.