Special This Original To Figure The Scrambling Of Index And Index Of Generalized Scrambling

Scrambling index is a very important research topic. Generalized scrambling indices of digraphs are generalizations of traditional scrambling index of primitive digraphs, with applications in memoryless communication systems. In this paper, we study the scram-bling index and the generalized scrambling indices of special primitive digraphs, including symmetric primitive digraphs and primitive minimally strong digraphs.In chapter1, we mostly introduce the background of research on the nonnegative square matrix and the graph, and then give some basic knowledge, relevant conclusions and the main results.In chapter2, we study two classes of symmetric primitive digraphs with loops, and obtain the scrambling indices and the generalized scrambling indices of the two special classes of digraphs.In chapter3, we investigate the scrambling indices of two primitive minimally strong digraphs.In chapter4, we characterize the lower scrambling indices and the bounds of the lower scrambling indices of the primitive minimally strong digraphs.