The Scrambling Exponent And Generalized Competition Exponent Of Four Primitive Digraphs

Combinatorial mathematics is a subject that researches discrete objects, and is widelyused. Graph theory is an important branch of combinatorial mathematics, and it is a veryuseful tool to solve geometry, number theory, operations research and optimization problemsin areas such as various combinations.Combining with graph theory and combinational theory, and through analyses of thevertex set which can be reached by a walk of length k from vertex in digraph, thescrambling indices, generalized scrambling indices and generalized competition indices ofsome special primitive digraphs are given.In chapter1, some basic concepts and research background of the combinatorialmathematics and graph theory are introduced. And at the same time, the concepts of thescrambling index, generalized scrambling index, generalized competition index and itsresearch status at home and abroad are introduced. At last, the main conclusions of this thesisare given.In chapter2, we discuss the scrambling indices of three special primitive digraphs.In chapter3, we study the generalized scrambling indices of three special primitivedigraphs.In chapter4, we characterize generalized scrambling indices and generalized competitionindices of a special primitive digraph.