The Scrambling Index And Generalized Competition Index Of Three Special 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 solving combinedoptimization problems. Graph theory is used in many fields such as information science,social sciences, economic administration.The scrambling index, generalized scrambling index and generalized competition indexof three special primitive digraphs have been researched in this dissertation.The chapter1is the introduction, including the theoretical significance and practicalapplication of the graph theory, the conceptions and research status of the scrambling indexand generalized competition index of the primitive digraph, and some conclusions in thisthesis.In chapter2, the scrambling index of a special primitive digraph which contains sixcycles is obtained.Chapter3considers the scrambling index, generalized scrambling index and generalizedcompetition index of a special primitive digraph which contains three cycles.Chapter4research the scrambling index and generalized competition index of a specialprimitive digraph which has a lot of cycles and one loop.