Sign Pattern Matrix Of Primitive Non-power Base And Broad-based Community

Sign pattern matrix is a very active research topic in combinatorial mathematics, one of the important reasons is that the study of sign pattern matrix in economics, biology, chemical, sociological and theories of computer science have extensive practical application. In this paper, we study the bases and the local bases for a special class of primitive non-powerful sign patterns.In chapter 1, we introduce the history of development on the sign pattern matrix, some methods used in our paper and our research problems and main results.In chapter 2, we obtained the bases for a class of n by n (n≥5 and n is odd) primitive non-powerful signed digraphs.In chapter 3, we firstly obtained the exponent of vertex for a class of n by n(n≥5 and n is odd) primitive non-powerful signed digraphs whose special vertex. Then given such graphic generalized primitive exponent. Finally through the analysis of a pair of SSSD walks in digraphs,we obtained the local of the special digraphs with previous conclusions.