Primitive Exponents Of Several Class Of Two-colored Digraphs

Combinatorial mathematics is also called combinatorial theory , combinatorial analysis orcombinatorics, algebra, number theory, topology, probability theory and otherdiscipline-based research tools, research background in computer science and informationscience, discrete structuresthe main object of study of a subject, a branch of mathematics.Graph theory as an independent discipline is an important branch of combinatorics.Non-negative matrix theory is a research direction in combinatorial matrix theory,Non-negative matrix theory is a research direction in combinatorial matrix theory, study thezero mode only depends on the matrix, and has nothing to do with the size of the matrixelement numerical nature, and depicts this matrix the zero mode shown a combination ofnature’s best tool is a directed graph. So the matrix and the Figure number and form linkages,the perfect combination of a model. Nonnegative matrix A can build correspondence relationswith the concomitant directed graph D(A), so we can solve some nonnegative matrixproblems using the knowledge of graph theory.In this article, we considered the exponents of a class of two-colored single double Intervaldirected cycles with loops, the primitive exponents of a class of two-colored digraphs withfive cycles. Its primary coverage is:In chapter 1, firstly, we introduce the relational concepts of graph and nonnegative matrix.Secondly, from the relation of graph and nonnegative property we introduce some elementaryknowledge and the domestic and foreign research survey of the primitive matrixes andprimitive exponents of directed digraph. Lastly, we propose our research problems.In chapter 2, we consider the exponents of a class of two-colored single double Intervaldirected cycles with loops. It’s uncolored digraph has n vertices and consist of one n-cycle ,(n-1)/22-cycles and n loops , we give some primitive conditions and the upper boundson the exponents .In chapter 3, we consider the primitive exponents of a class of two-colored digraphs with fivecycles. It’s uncolored digraph has n vertices and consist of one n-cycle , one (n-1)-cycle ,one(n-2)-cycle , one 3-cycle and one 2-cycle. we give some primitive conditions and the upperbounds on the exponents.