The Original Special Scrambling To Figure Index Number Can Not Be Given The Power Base Of A Directed Graph

Combinatorial mathematics, also called combinatoric. The subject is associated with the theory of mathematics and probability calculation in the beginning. In modern times, because of the appear of the computers, combinatorial mathematics developed rapidly and becamed an important branch of mathematics. The development changed the situation which analysis and algebra occupied the dominance in traditional mathematics. In recent years, due to important applications of the combinatorial mathematics in various fields, this branch of mathematics has been highly valued in today’s world, and the scrambling index has becomed one of a emerging research hot spot in the combinatorial mathematics.In this dissertation, the scrambling indices of a special class of primitive diagraphs which contains exactly two circles of length s and one circle of length p and the base of non-powerful signed diagraph which are based on such primitive diagraphs are discussed. The main content is as follows:PartⅠ:Introduced the the research background, theoretical significance and the practical application value, and on this basis, described initially the relationships and the relative definitions of the primitive digraph and the nonnegative matrix.Part Ⅱ:Further introduced the scrambling index of the primitive diagraph and the base of non-powerful signed diagraph which is based on such a primitive diagraph in detail, including the basic concepts and research status. At the same time, this part expounds the main content of this paper.Part Ⅲ:Researched and discussed the scrambling indices of two primitive diagraphs and the bases of non-powerful signed diagraphs which are based on such primitive diagraphs in detail, and obtained the scrambling indices and the bases of non-powerful signed diagraphs respectively.Part Ⅳ:Researched the scrambling indices of a special class of primitive diagraphs which contain exactly two circles of length s and one circle of length p. By analyzing the characteristic of diagraphs and combining the definition and properties of the scrambling index, then the scrambling indices of such special primitive diagraphs are concluded.