Special This Original To The Figure Of Scrambling And General Competition Index

The combinatorics is a mathematics developed rapidly since the advent of the computer.It has an extremely important role not only in basic mathematics study but also widelyapplications in other other subjects, such as computer science, coding and cryptography, physics,chemistry, biology and so on.In this paper, we study the scrambling index and competition index of no Hamilton cycleprimitive digraphs of order n. The main content is as follows:Part I Introduction of the history and significance of combinatorics and graph theory, andthe relationship and the relative definitions of digraph and nonnegative matrix. On this basis,carried out a detailed introduction to the scrambling index and generalized competition indexof primitive digraph, containing basic concepts, as well as domestic and international researchstatus. Also described the main content of this paper.Part II The scrambling index of two special primitive digraphs are discussed in detail,respectively. The exact values of their scrambling indexes and generalized scrambling indexare obtained.Part III Obtain the exact value of their generalized competition indexes by therelationship among exponent, scrambling index and generalized competition index of the twoprimitive digraphs of order n.