The Scrambling Index And M - Competition Index Of The Three Original Primitive Graphs

Graph theory is an important branch in the research area of combinatorial mathematics,which is mainly about the study of graphs. It is a very useful tool to solve operations research,geometry, and optimization problems. Meanwhile, a series of its research results also widely apply in information technology, social science, etc.In this thesis, we mainly study the three types of primitive digraphs, one of which the scrambling index and generalized scrambling index are given; The m-competition index of the other two classes of primitive digraphs are given respectively.In chapter one, the history of development and research status about combinatorial mathematics are chiefly introduced. The basic concepts, major achievements and the main conclusions of this thesis are provided.In chapter two, the scrambling index and generalized scrambling indices of the primitive digraph with two s-cycles and two(s-1)-cycles are given.In chapter three, the m-competition index and the generalized scrambling indices of a class of primitive digraph with two(s-1)-cycles and s s-cycles are given.In chapter four, the m-competition index of a class of primitive digraphs with a n-cycle and two s-cycles, where sn??12 are given.