The Symbolic Control Number Of The Graph

Developments of the control theory in graph theory expended the optimization problem in graph theory.In this paper,based on the research of the signed domination number properties of graphs,we obtain some signed domination number of some graphs and some upper and lower bounds of the signed domination number of some special cases,the signed domination number of the cartesian products of two graphs and also signed k domination number of graphs.First of all,we will mainly introduces some symbols,some basic concepts and definitions,some important conclusion and lemma from the graph theory which will use in this paper.Secondly,based on the related definition and lemma of the signed domination number,we will determine some upper and lower bounds about it,and research the relationship among maximum degree,minimum degree and signed domination number.Finally,we will introduce some concepts and the related lemma conclusion of the signed k-domination number and discuss some upper bound about it.