Several Types Of Primitive Non-power Given Broad Base, A Directed Graph

Graph theory is a branch of combinatorial mathematics. It has been widely applied in many different fields, such as physics, chemistry, operation research, computer science, information theory, cybernetics, network theory, social science as well as economical management.The signed digraph can build correspondence relations with the concomitant sign pattern matrix. So about the research of sign pattern matrix can be transformed into the research of signed digraphs, we can solve some sign pattern matrix problems using the knowledge of graph theory.In this paper, we study the local bases of some class primitive non-powerful, signed digraphs. The local bases of the digraphs were derived using the primitive digraph analysis associated with SSSD walks and Frobenius.In chapter 1, firstly, we outline the history of development on the graph theory. Secondly, the relationship of signed digraphs and the sign pattern matrices was introduced.In chapter 2, some basic definition of signed digraphs,main results,the history and current situation on the signed digraphs and our works were introduced.In chapter 3, the local bases of three class primitive non-powerful signed digraphs were discussed separately.