Primitive Power Assignment Not Directed Graph Base And General Base

Graph theory is a very important foundational question in combinatorial mathematics,it has a wide application in many subjects as economics!Physics, Chemistry, computer,sociology and so on. There are one to one corresponding relation between the signed directedgraph and sign pattern matrix. So the research of sign pattern matrix but also the needof social development.In this paper,we study the bases and the local bases of sign patternmatrix, and we give the boundary line of several kinds of primitive non-powerful signeddirected graph’s base.In the first chapter,we introduce the history of development on the sign pattern ma-trix,the research progress of the signed digraphs,and some basic knowledge,main conclusions.In the second chapter, we study the base of primitive non-powerful signed digraphmatrix which contains two (n-2t-1) circles and a (n-2t) , and show the bounds on thebases.In the third chapter and fourth chapter, we study two classes of primitive non-powerfulsigned digraphs, and obtain the local bases of the two classes of digraphs respectively.