Scrambling Index And Generalized Scrambling Exponent Of Three Primitive Digraphs

Combinatorial mathematics is an important branch of mathematics. Graph theory whichhas developed rapidly in recent years is a branch of combinatoial mathematics. Since thecomputer appeared, the graph theory has become a significant method to solve thecombinatorial mathematics problems. Graph theory is used in a wide range of fields such asphysics, chemistry, biological science, information technology, the social science and so on.The focus of this thesis is to research the scrambling index and generalized scramblingindices of three primitive digraphs.In chapter1, we introduce the related theory and the research significance ofcombinatorial mathematics and graph theory, and summarize the concepts and the researchstatus of the scrambling index and generalized scrambling indices of the primitive digraph.Also describe the main conclusions of this thesis.In chapter2, we research the scrambling index and generalized scrambling indices of aprimitive digraph which contains five cycles.In chapter3, we research the scrambling index and generalized scrambling indices of aprimitive digraph which contains one n-cycles and two s-cycles.In chapter4, we research the scrambling index and generalized scrambling indices of aspecial primitive digraph.