The Scrambling Index And M-Competition Index Of Two Special Classes Of Primitive Digraphs

As a branch of combinatorial mathematics, the combinatorial property in graph theory played a very important role in both math itself and a large variety of social activities. This article obtained a upper bound of the Scrambling index of a class of primitive digraphs and the Scrambling index and m-Competition index of a special class of primitive digraphs with one loop by using some methods of number theory based on the characteristic of those digraphs.In chapter1we introduce the basic knowledge of graph theory, which including the concept of primitive digraphs, scrambling index and m-competition index. We also provide the newest research development and the main conclusions of this article.In Chapter2we focus on the research of the upper bound of a special class of primitive digraphs.In Chapter3we first show the upper bound of the Scrambling index, index set and digraphs that reach the upper bound of a special class of primitive digraphs with one loop. Then we show the upper bound of the m-Competition index and digraphs that reach that bound of that class of digraphs.