The Scrambling Exponent And Generalized Competition Exponent Of Three N - Order Primitive Digraphs

Graph theory is an important branch of combinatorial mathematics. Along with theoccurrence of the computer, the graph theory becomes a powerful tool for solvingcombinatorial problems. Graph theory is used in many fields such as information science,social sciences, economic administration.By analyzing the set of points that each point in digraph got to by directed walks oflength t, and combining with the knowledge of graph theory and set operation, thescrambling indices, generalized scrambling indices and generalized competition indices ofthree special primitive digraphs are given. The main content of this paper are as follows:The first chapter introduces the significance of combinatorial mathematics and the graphtheory, then introduces the conceptions and research status of the scrambling index,generalized scrambling indices and generalized competition index. Finally some conclusionsof this thesis are given.The second chapter studies the scrambling index and the generalized scrambling indicesof a primitive digraph which contains four cycles.The third chapter considers the scrambling index and generalized competition index of aprimitive digraph which contains three cycles.The fourth chapter researches the scrambling index and generalized scrambling indicesof a special primitive digraph.