Study On Signed Domination Number Of Graphs

With the fast going of the Modern Technology and Computer Science, Graph Theory take an important place in many disciplines and fields. The domination theory as one of the important research aspects of Graph Theory, also get more attention and development. In recent years, the definition and form of the domination theory are more diversified, and it futher promote its application in the practical problem. Since the domination problem is a NP-complete problem, the exact estimations of upper and lower bounds of the domination number are a matter of interest at present.In chapter1, besides introducing the corresponding concepts and background of Graph Theory, we mainly present the terminology and development history of the domination theory. In chapter2, we firstly give the definition and former research development of Negative k-subdecision Number; By using the new methed or changing the parameters and parameter ranges, some new bounds are given and some known results are extended. In chapter3, we firstly introduce the concept and results on Strong Signed Domination Number; Then we get the new lower bounds of the Strong Signed Domination Number by applying new parameters. Futhermore, we prove the new uppers and lower bounds are sharp. In the end, we summarize the results in this thesis, and provide some problems that are worth of further research.