Research On Some Domination Problems Of Special Graphs

Graph theory is an important branch of applied mathematics.It transforms many complex problems in life into graphic problems between points and lines,and makes many complex problems into simplification.There are a lot of models that can be abstracted into graph theory problems in many areas of our daily life,which also promotes the development of graph theory.The domination theory of graph is an important branch of graph theory.It is not only widely used in the field of graph theory itself,but also has a broad application background in other disciplines and fields.In recent years,a large number of scientific research achievements on graph domination theory have emerged.Some new domination concepts have been pro-posed.Signed domination?signed edge domination and total signed domination of graphs axe all generalizations of classical domination problems.This makes research on signed domination numbers,signed edge domination numbers and total signed domination number of graphs become the problems concerned by people.In graph domination theory,it is a basic problem to determine the domination number of a graph,so it is very important to determine the upper and lower bounds of the domination number of a graph and the exact domination number of some special graphs.In this paper,we study the signed domination and signed edge domination of two kinds of graphs in which two adjacent cycles of cycles are merged in n copies by a point or an edge,and give their signed domination numbers and signed edge domination numbers.At the same time,a new kind of domination weak total signed domination will be given.And the weak total signed domination of Pn and Cn will be studied,and their weak total signed domination numbers will be given.