Research On The Fractional Domination In Graphs

In recent years, with the rapid development of computer、communication、network and other technical, the digital technology on the discrete structure is more and more attention.The level of the figure labeling improved continually. The graph theory of some related contents constantly enriched. This essay mainly aims at the Fractional domination in graphs,and at the same time, it enriches and perfects the content of the field.This essay mainly researches the problem of the discrete structure, namely the special dot domination in graphs,(Fractional domination). For solving practical needs, this essay employs the Fractional domination to label. The Fractional views, understands and studies digital problem of graphs from the point of function. Firstly, this essay introduce the development background, application field and research direction of the Fractional domination in graphs, then, on the basis of the concept of the Fractional domination, we do further research on the Fractional total domination, the Fractional edge domination, the Fractional edge total domination and the Fractional star domination, it improves and perfects the domination theory. The research is the combination of theory and practical problems. It provides effective and reliable theoretical basis and practical mathematical model for the practical problem, and at the same time, more and more practical problem can be solved in a more concise way.In the end, the research content will make the domination theory in graphs more and more widely, it is the important element to link the theory and the practice. Meanwhile, this study makes the theory richer in practice, and at the same time, It makes the domination theory moving towards an applied subjects constantly.