Research On The Bases On Two Classes Of Primitive Non-powerful Signed Digraphs

Sign pattern matrix is very active in the research topics of combinatorial matrix theory, and one of the main reasons is that it has wide application in many subjects, such as economics,biology,chemistry,sociology and computer science. In this paper, we study two kinds of primitive non-powerful signed digraph mainly.In chapter 1, we introduce the research background of the development on the sign pattern matrices, some basic concepts of sign pattern matrix and digraph, our research problems and main results.In chapter 2, the relevant operator of the upper bound of the exponent,the local exponent,the base and the local base was given, besides which ,we introduced Frobenius number and other knowledge of the digraph in the chapterIn chapter 3, By analyzing matrix and diagrams, we study the question of primitive non-powerful signed digraph with two simple cycles and with three simple cycles. By using Frobeniusnumber to study lower bound of the base and the local base and a pair of SSSD walks or the conclusion of the existing to study upper bound of the base and the local base, we obtain the equality cases of the base and the local base for two kind of digraphs.