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

Combinatorial mathematics study long time,it is a key branch of mathematics,mainly by the discrete structure as the research object.Graph theory origin early,is an important branch of discrete math is the theory of the study are connected by a line of point set.With the continuous development of graph theory, the scrambling indices,the generalized scrambling indices and the generalized scrambling indices become a popular research topic in graph theory.Combining with graph theory and combinatorial theory, and through analyses of the vertex set which can be reached by a walk of length k from each vertex in digraph, the scrambling indices and the generalized scrambling indices of two kinds of primitive digraphs of order n are given and the m-competition indices of the primitive digraph of order n are given. The main content of this paper are as follows:In the first chapter, it introduces the status of the scrambling index, generalized scrambling indices and generalized competition index. Some conclusions are given.In the second chapter, it studies the scrambling index and the generalized scrambling indices of two special primitive digraphs with n-cycle and s-cycles.The third chapter considers m-competition index of a special primitive digraph.