Including Double Color Ring To Ruby Roth Study Of The Original Index

Graph theory is an emerging discipline.It is an important branch of the combination ofmathematics and it is now probably less than three hundred years of history. Non-negativematrix theory is a research direction in combinatorial matrix theory, which studies the naturethat only depends on the matrix and has nothing to do with the magnitude of matrixelements.The directed graph is the best tool to characterize this nature. This non-negativematrix and its corresponding adjoint establish a one to one relationship between a directedgraph, we can use the knowledge of graph theory to solve some problems of non-negativematrix.The main content of this article is:In chapter 1，firstly, we introduce the history of development on the primitive exponents,some basic knowledge .Secondly, we introduce the domestic and foreign research survey ofthe primitive matrixes and primitive exponents of directed digraph．Lastly,we propose ourresearch problems.In chapter 2, we consider the special two-colored digraphs whose uncolored digraph hasn vertices and consist of one n-cycle, one (n-1)-cycle, and n loops, and we give someprimitive conditions and the upper bounds on the exponents.In chapter 3, we consider the special two-colored digraphs whose uncolored digraph hasn vertices and consist of one n-cycle, two (n-1)-cycles, and n loops .We give the primitiveconditions and the upper bounds on the exponents.